DCDiego Córdoba
Diego Córdoba
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Diego Córdoba has a total of 68 co-authors. Here are the top co-authors by number of shared publications:
- Francisco Gancedo
Departamento de Análisis Matemático & IMUS, Universidad de Sevilla, Sevilla, Spain
31 shared publications - Charles Fefferman
Department of Mathematics, Princeton University, Princeton, USA
19 shared publications - Javier Gómez-Serrano
Princeton University
15 shared publications - Angel Castro
Instituto de Ciencias Matemáticas ICMAT-CSIC-UAM-UCM-UC3M 28049 Madrid Spain
14 shared publications - Francisco Gancedo12 shared publications
Charles Fefferman
Princeton University
11 shared publications
Latest Publications
- Open Access
- 11 May 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (3) , 38
Finite Time Blow-Up for the Hypodissipative Navier Stokes Equations with a Force in $L^1_t C_x^{1,\epsilon }\cap L^{\infty }_{t} L^{2}_{x}$In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $$|\nabla |^{\alpha }$$ for any $$\alpha \in [0, \alpha _0)$$ ( $$\alpha _0 = \frac{22-8\sqrt{7}}{9} > 0$$ ). We construct solutions in $$\mathbb {R}^3\times [0,T]$$ with a finite $$T>0$$ and with an external forcing which is in $$L^1_t([0, T]) C_x^{1,\epsilon }\cap L^{\infty }_{t} L^{2}_{x}$$ , such that for each time $$t \in [0, T)$$ , the velocity u is in the space $$C^\infty \cap L^2$$ and such that as the time t approaches the blow-up moment T , the integral $$\int _0^t |\nabla u| \text {d}s$$ tends to infinity. Since this result lays in a well-posedness class, the blow-up is generated by the dynamics of the equation and not by the force itself. This is the first blow-up result for hypodissipative Navier–Stokes in a well-posedness class.- 11 May 2026
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 250 (3) , 38
Open AccessFinite Time Blow-Up for the Hypodissipative Navier Stokes Equations with a Force in $L^1_t C_x^{1,\epsilon }\cap L^{\infty }_{t} L^{2}_{x}$In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $$|\nabla |^{\alpha }$$ for any $$\alpha \in [0, \alpha _0)$$ ( $$\alpha _0 = \frac{22-8\sqrt{7}}{9} > 0$$ ). We construct solutions in $$\mathbb {R}^3\times [0,T]$$ with a finite $$T>0$$ and with an external forcing which is in $$L^1_t([0, T]) C_x^{1,\epsilon }\cap L^{\infty }_{t} L^{2}_{x}$$ , such that for each time $$t \in [0, T)$$ , the velocity u is in the space $$C^\infty \cap L^2$$ and such that as the time t approaches the blow-up moment T , the integral $$\int _0^t |\nabla u| \text {d}s$$ tends to infinity. Since this result lays in a well-posedness class, the blow-up is generated by the dynamics of the equation and not by the force itself. This is the first blow-up result for hypodissipative Navier–Stokes in a well-posedness class. - Open Access
- 7 July 2025
- Published by Springer Nature in Annals of PDE
- Vol. 11 (2) , 1-56
Finite Time Singularities to the 3D Incompressible Euler Equations for Solutions in$\:C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,\alpha}\cap L^2$We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in $$\mathbb{R}^3\times [-T,0]$$ such that the velocity is in the space $$C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,\alpha}\cap L^2$$ where $$0 < \alpha \ll 1$$ for times $$t\in (-T,0)$$ and is not $$C^1$$ at time 0.- 7 July 2025
- Published by Springer Nature in Annals of PDE
- Vol. 11 (2) , 1-56
Open AccessFinite Time Singularities to the 3D Incompressible Euler Equations for Solutions in$\:C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,\alpha}\cap L^2$We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in $$\mathbb{R}^3\times [-T,0]$$ such that the velocity is in the space $$C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,\alpha}\cap L^2$$ where $$0 < \alpha \ll 1$$ for times $$t\in (-T,0)$$ and is not $$C^1$$ at time 0. - Open AccessNon Existence and Strong Ill-Posedness in $H^2$ for the Stable IPM EquationWe prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small $H^2(\mathbb{R}^2)$ perturbations of the linearly stable profile $-x_2$. A remarkable novelty of the proof is the construction of an $H^2$ perturbation, which solves the IPM equation and neutralizes the stabilizing effect of the background profile near the origin, where a strong deformation leading to non-existence in $H^2$ is created. This strong deformation is achieved through an iterative procedure inspired by the work of Córdoba and Martínez-Zoroa (Adv. Math. 2022). However, several differences - beyond purely technical aspects - arise due to the anisotropic and, more importantly, to the partially dissipative nature of the equation, adding further challenges to the analysis.Open AccessNon Existence and Strong Ill-Posedness in $H^2$ for the Stable IPM EquationWe prove the non-existence and strong ill-posedness of the Incompressible Porous Media (IPM) equation for initial data that are small $H^2(\mathbb{R}^2)$ perturbations of the linearly stable profile $-x_2$. A remarkable novelty of the proof is the construction of an $H^2$ perturbation, which solves the IPM equation and neutralizes the stabilizing effect of the background profile near the origin, where a strong deformation leading to non-existence in $H^2$ is created. This strong deformation is achieved through an iterative procedure inspired by the work of Córdoba and Martínez-Zoroa (Adv. Math. 2022). However, several differences - beyond purely technical aspects - arise due to the anisotropic and, more importantly, to the partially dissipative nature of the equation, adding further challenges to the analysis.
- Open Access
- 25 September 2024
- Published by Springer Nature in Annals of PDE
- Vol. 10 (2) , 1-52
Global Unique Solutions with Instantaneous Loss of Regularity for SQG with Fractional Diffusion
In this work we construct global unique solutions of the dissipative Surface quasi-geostrophic equation ( $$\alpha $$ -SQG) that lose regularity instantly when there is super-critical fractional diffusion.- 25 September 2024
- Published by Springer Nature in Annals of PDE
- Vol. 10 (2) , 1-52
Open AccessGlobal Unique Solutions with Instantaneous Loss of Regularity for SQG with Fractional Diffusion
In this work we construct global unique solutions of the dissipative Surface quasi-geostrophic equation ( $$\alpha $$ -SQG) that lose regularity instantly when there is super-critical fractional diffusion. - Top Cited PapersOpen Access
- 1 July 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (7) , 1-53
Non-existence and Strong lll-posedness in $C^{k,\beta }$ for the Generalized Surface Quasi-geostrophic EquationWe consider solutions to the generalized Surface Quasi-geostrophic equation ( $$\gamma $$ -SQG) when the velocity is more singular than the active scalar function (i.e. $$\gamma \in (0,1)$$ ). In this paper we establish strong ill-posedness in $$C^{k,\beta }$$ ( $$k\ge 1$$ , $$\beta \in (0,1]$$ and $$k+\beta >1+\gamma $$ ) and we also construct solutions in $$\mathbb {R}^2$$ that initially are in $$C^{k,\beta }\cap L^2$$ but are not in $$C^{k,\beta }$$ for $$t>0$$ . Furthermore these solutions stay in $$H^{k+\beta +1-2\delta }$$ for some small $$\delta $$ and an arbitrarily long time.- 1 July 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (7) , 1-53
Top Cited PapersOpen AccessNon-existence and Strong lll-posedness in $C^{k,\beta }$ for the Generalized Surface Quasi-geostrophic EquationWe consider solutions to the generalized Surface Quasi-geostrophic equation ( $$\gamma $$ -SQG) when the velocity is more singular than the active scalar function (i.e. $$\gamma \in (0,1)$$ ). In this paper we establish strong ill-posedness in $$C^{k,\beta }$$ ( $$k\ge 1$$ , $$\beta \in (0,1]$$ and $$k+\beta >1+\gamma $$ ) and we also construct solutions in $$\mathbb {R}^2$$ that initially are in $$C^{k,\beta }\cap L^2$$ but are not in $$C^{k,\beta }$$ for $$t>0$$ . Furthermore these solutions stay in $$H^{k+\beta +1-2\delta }$$ for some small $$\delta $$ and an arbitrarily long time. - Open Access
- 11 November 2023
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 16 (9) , 2109-2145
Stability of traveling waves for the Burgers–Hilbert equation
We consider smooth solutions of the Burgers-Hilbert equation that are a small perturbation δ from a global periodic traveling wave with small amplitude ϵ. We use a modified energy method to prove the existence time of smooth solutions on a time scale of 1/(ϵδ), with 0 < δ ≪ ϵ ≪ 1, and on a time scale of ϵ/δ 2 , with 0 < δ ≪ ϵ 2 ≪ 1. Moreover, we show that the traveling wave exists for an amplitude ϵ in the range (0, ϵ *), with ϵ * ∼ 0.23, and fails to exist for ϵ > 2/e.
- 11 November 2023
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 16 (9) , 2109-2145
Open AccessStability of traveling waves for the Burgers–Hilbert equation
We consider smooth solutions of the Burgers-Hilbert equation that are a small perturbation δ from a global periodic traveling wave with small amplitude ϵ. We use a modified energy method to prove the existence time of smooth solutions on a time scale of 1/(ϵδ), with 0 < δ ≪ ϵ ≪ 1, and on a time scale of ϵ/δ 2 , with 0 < δ ≪ ϵ 2 ≪ 1. Moreover, we show that the traveling wave exists for an amplitude ϵ in the range (0, ϵ *), with ϵ * ∼ 0.23, and fails to exist for ϵ > 2/e.
- Open Access
Finite-time singularity formation for angled-crested water waves
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a corner, it remains a corner but generically its angle changes. Using a characterization of the asymptotic behavior of the fluid near a corner that follows from our a priori energy estimates, we show the existence of initial data in these spaces for which the fluid becomes singular in finite time.
Open AccessFinite-time singularity formation for angled-crested water waves
We show that the water waves system is locally wellposed in weighted Sobolev spaces which allow for interfaces with corners. No symmetry assumptions are required. These singular points are not rigid: if the initial interface exhibits a corner, it remains a corner but generically its angle changes. Using a characterization of the asymptotic behavior of the fluid near a corner that follows from our a priori energy estimates, we show the existence of initial data in these spaces for which the fluid becomes singular in finite time.
- Open AccessFinite time singularities to the 3D incompressible Euler equations for solutions in $C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,α}\cap L^2$We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in $\mathbb{R}^3\times [-T,0]$ such that the velocity is in the space $C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,α}\cap L^2$ for times $t\in (-T,0)$ and is not $C^1$ at time 0.Open AccessFinite time singularities to the 3D incompressible Euler equations for solutions in $C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,α}\cap L^2$We introduce a novel mechanism that reveals finite time singularities within the 1D De Gregorio model and the 3D incompressible Euler equations. Remarkably, we do not construct our blow up using self-similar coordinates, but build it from infinitely many regions with vorticity, separated by vortex-free regions in between. It yields solutions of the 3D incompressible Euler equations in $\mathbb{R}^3\times [-T,0]$ such that the velocity is in the space $C^{\infty}(\mathbb{R}^3 \setminus \{0\})\cap C^{1,α}\cap L^2$ for times $t\in (-T,0)$ and is not $C^1$ at time 0.
- Open AccessBlow-up for the incompressible 3D-Euler equations with uniform $C^{1,\frac{1}{2}-ε}\cap L^2$ forceThis paper presents a novel approach to establish a blow-up mechanism for the forced 3D incompressible Euler equations, with a specific focus on non-axisymmetric solutions. We construct solutions on $\mathbb{R}^3$ within the function space $C^{3,\frac12}\cap L^2$ for the time interval $[0, T)$, where $T > 0$ is finite, subject to a uniform force in $C^{1,\frac12 -ε}\cap L^2$. Remarkably, our methodology results in a blow-up: as the time $t$ approaches the blow-up moment $T$, the integral $\int_0^t |\nabla u| ds$ tends to infinity, all while preserving the solution's smoothness throughout, except at the origin. In the process of our blow-up construction, self-similar coordinates are not utilized and we are able to treat solutions beyond the $C^{1,\frac13+}$ threshold regularity of axy-symmetric solutions without swirl.Open AccessBlow-up for the incompressible 3D-Euler equations with uniform $C^{1,\frac{1}{2}-ε}\cap L^2$ forceThis paper presents a novel approach to establish a blow-up mechanism for the forced 3D incompressible Euler equations, with a specific focus on non-axisymmetric solutions. We construct solutions on $\mathbb{R}^3$ within the function space $C^{3,\frac12}\cap L^2$ for the time interval $[0, T)$, where $T > 0$ is finite, subject to a uniform force in $C^{1,\frac12 -ε}\cap L^2$. Remarkably, our methodology results in a blow-up: as the time $t$ approaches the blow-up moment $T$, the integral $\int_0^t |\nabla u| ds$ tends to infinity, all while preserving the solution's smoothness throughout, except at the origin. In the process of our blow-up construction, self-similar coordinates are not utilized and we are able to treat solutions beyond the $C^{1,\frac13+}$ threshold regularity of axy-symmetric solutions without swirl.
- Open Access
Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations
We construct solutions of the 2D incompressible Euler equations in $\mathds{R}^2\times [0,\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^\beta$ for $1<\beta1+\frac{(3-\beta)(\beta-1)}{2 - (\beta-1)^2}$ for $0<t<\infty$. These solutions are not in the Yudovich class, but they exists globally in time and they are unique in a determined family of classical solutions.Open AccessInstantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations
We construct solutions of the 2D incompressible Euler equations in $\mathds{R}^2\times [0,\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^\beta$ for $1<\beta1+\frac{(3-\beta)(\beta-1)}{2 - (\beta-1)^2}$ for $0<t<\infty$. These solutions are not in the Yudovich class, but they exists globally in time and they are unique in a determined family of classical solutions.