Monica Musso
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Monica Musso has a total of 71 co-authors. Here are the top co-authors by number of shared publications:
- Manuel del Pino
Department of Mathematical Sciences, University of Bath, Bath, UK
55 shared publications - Juncheng Wei
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
32 shared publications - Angela Pistoia
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Roma, Italy
19 shared publications - Juan Dávila
Department of Mathematical Sciences, University of Bath, Bath, UK
15 shared publications Juncheng Wei
10 shared publications- Jean Dolbeault
CEREMADE Centre de Recherche en Mathématiques de la Décision (CNRS UMR n • 7534) PSL University Université Paris-Dauphine Place de Lattre de Tassigny 75775 Paris 16 France
6 shared publications
Latest Publications
- Top Cited Papers
- 13 March 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
Global-in-time vortex configurations for the $2$D Euler equations
We consider the problem of finding a solution to the incompressible Euler equations \omega_{t} + v\cdot \nabla \omega = 0 \ \hbox{in }\mathbb{R}^{2} \times (0,\infty), \quad v(x,t) = \frac{1}{2\pi}\int_{\mathbb{R^2}}\frac{(y-x)^{\perp}}{|y-x|^{2}}\omega (y,t)\, dy that is close to a superposition of travelling vortices as t\to \infty . We employ a constructive approach by gluing classical travelling waves: at main order two vortex-antivortex pairs. Each pair consists of two vortices a distance 2q from each other, with wave speed c , moving in the positive and negative x_{1} directions respectively. More precisely, we find an initial condition that leads to a 4-vortex solution of the form \omega (x,t) = \omega_{0}(x-cte_{1}) - \omega_{0} ( x+ cte_{1}) + o(1) \quad \hbox{as }t\to\infty, where \omega_{0}( x ) = \frac{1}{\varepsilon^{2}}W \biggl ( \frac{x-q}{\varepsilon} \biggr ) - \frac{1}{\varepsilon^{2}}W \biggl ( \frac{x+q}{\varepsilon} \biggr ) + o(1) \quad \hbox{as }\varepsilon \to 0 and W(y) is a certain fixed smooth profile, radially symmetric, positive in the unit disk and zero outside.
- 13 March 2026
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
Top Cited PapersGlobal-in-time vortex configurations for the $2$D Euler equations
We consider the problem of finding a solution to the incompressible Euler equations \omega_{t} + v\cdot \nabla \omega = 0 \ \hbox{in }\mathbb{R}^{2} \times (0,\infty), \quad v(x,t) = \frac{1}{2\pi}\int_{\mathbb{R^2}}\frac{(y-x)^{\perp}}{|y-x|^{2}}\omega (y,t)\, dy that is close to a superposition of travelling vortices as t\to \infty . We employ a constructive approach by gluing classical travelling waves: at main order two vortex-antivortex pairs. Each pair consists of two vortices a distance 2q from each other, with wave speed c , moving in the positive and negative x_{1} directions respectively. More precisely, we find an initial condition that leads to a 4-vortex solution of the form \omega (x,t) = \omega_{0}(x-cte_{1}) - \omega_{0} ( x+ cte_{1}) + o(1) \quad \hbox{as }t\to\infty, where \omega_{0}( x ) = \frac{1}{\varepsilon^{2}}W \biggl ( \frac{x-q}{\varepsilon} \biggr ) - \frac{1}{\varepsilon^{2}}W \biggl ( \frac{x+q}{\varepsilon} \biggr ) + o(1) \quad \hbox{as }\varepsilon \to 0 and W(y) is a certain fixed smooth profile, radially symmetric, positive in the unit disk and zero outside.
- 1 January 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 394 (1) , 25
Nearly parallel helical vortex filaments in the three-dimensional Euler equations
- 1 January 2026
- Published by Springer Nature in Mathematische Annalen
- Vol. 394 (1) , 25
Nearly parallel helical vortex filaments in the three-dimensional Euler equations
- Open AccessHelical vortex filaments with compactly supported cross-sectional vorticity for the incompressible Euler equations in $\mathbb{R}^3$We revisit the vortex filament conjecture for three-dimensional inviscid and incompressible Euler flows with helical symmetry and no swirl. Using gluing arguments, we provide the first construction of a smooth helical vortex filament in the whole space $\mathbb{R}^3$ whose cross-sectional vorticity is compactly supported in $\mathbb{R}^2$ for all times. The construction extends to a multi-vortex solution comprising several helical filaments arranged along a regular polygon. Our approach yields fine asymptotics for the vorticity cores, thus improving related variational results for smooth solutions in bounded helical domains and infinite pipes, as well as non-smooth vortex patches in the whole space.Open AccessHelical vortex filaments with compactly supported cross-sectional vorticity for the incompressible Euler equations in $\mathbb{R}^3$We revisit the vortex filament conjecture for three-dimensional inviscid and incompressible Euler flows with helical symmetry and no swirl. Using gluing arguments, we provide the first construction of a smooth helical vortex filament in the whole space $\mathbb{R}^3$ whose cross-sectional vorticity is compactly supported in $\mathbb{R}^2$ for all times. The construction extends to a multi-vortex solution comprising several helical filaments arranged along a regular polygon. Our approach yields fine asymptotics for the vorticity cores, thus improving related variational results for smooth solutions in bounded helical domains and infinite pipes, as well as non-smooth vortex patches in the whole space.
- Open Access
Solvability for the Ginzburg-Landau equation linearized at the degree-one vortex
We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution $W(x)=w(r)e^{iθ}$. Using explicit representation formulae for the Fourier modes in $θ$, we obtain sharp estimates for the inverse of the linearized operator which hold for a large class of right-hand sides. This theory can be applied, for example, to estimate the inverse after dropping the usual orthogonality conditions.Open AccessSolvability for the Ginzburg-Landau equation linearized at the degree-one vortex
We consider the Ginzburg-Landau equation in the plane linearized around the standard degree-one vortex solution $W(x)=w(r)e^{iθ}$. Using explicit representation formulae for the Fourier modes in $θ$, we obtain sharp estimates for the inverse of the linearized operator which hold for a large class of right-hand sides. This theory can be applied, for example, to estimate the inverse after dropping the usual orthogonality conditions. - Open Access
Overhanging solitary water waves
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless gravitational constant $g>0$ is sufficiently small. Our construction involves combining three explicit solutions to related problems: a disk of fluid in rigid rotation, a linear shear flow in a strip, and a rescaled version of an exceptional domain discovered by Hauswirth, Hélein, and Pacard \cite{hauswirth-helein-pacard}. The method developed here is related to the construction of constant mean curvature surfaces through gluing.Open AccessOverhanging solitary water waves
We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless gravitational constant $g>0$ is sufficiently small. Our construction involves combining three explicit solutions to related problems: a disk of fluid in rigid rotation, a linear shear flow in a strip, and a rescaled version of an exceptional domain discovered by Hauswirth, Hélein, and Pacard \cite{hauswirth-helein-pacard}. The method developed here is related to the construction of constant mean curvature surfaces through gluing. - Open Access
- 18 June 2024
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 248 (4) , 1-154
Existence and Stability of Infinite Time Blow-Up in the Keller–Segel System
Perhaps the most classical diffusion model for chemotaxis is the Keller–Segel system We consider the critical mass case $$\int _{{\mathbb {R}}^2} u_0(x)\, \textrm{d}x = 8\pi $$ , which corresponds to the exact threshold between finite-time blow-up and self-similar diffusion towards zero. We find a radial function $$u_0^*$$ with mass $$8\pi $$ such that for any initial condition $$u_0$$ sufficiently close to $$u_0^*$$ and mass $$8\pi $$ , the solution u(x, t) of ( $$*$$ ) is globally defined and blows-up in infinite time. As $$t\rightarrow +\infty $$ it has the approximate profile $$\begin{aligned} u(x,t) \approx \frac{1}{\lambda ^2(t)} U\left( \frac{x-\xi (t)}{\lambda (t)} \right) , \quad U(y)= \frac{8}{(1+|y|^2)^2}, \end{aligned}$$ where $$\lambda (t) \approx \frac{c}{\sqrt{\log t}}$$ , $$\xi (t)\rightarrow q$$ for some $$c>0$$ and $$q\in {\mathbb {R}}^2$$ . This result affirmatively answers the nonradial stability conjecture raised in Ghoul and Masmoudi (Commun Pure Appl Math 71:1957–2015, 2018).- 18 June 2024
- Published by Springer Nature in Archive for Rational Mechanics and Analysis
- Vol. 248 (4) , 1-154
Open AccessExistence and Stability of Infinite Time Blow-Up in the Keller–Segel System
Perhaps the most classical diffusion model for chemotaxis is the Keller–Segel system We consider the critical mass case $$\int _{{\mathbb {R}}^2} u_0(x)\, \textrm{d}x = 8\pi $$ , which corresponds to the exact threshold between finite-time blow-up and self-similar diffusion towards zero. We find a radial function $$u_0^*$$ with mass $$8\pi $$ such that for any initial condition $$u_0$$ sufficiently close to $$u_0^*$$ and mass $$8\pi $$ , the solution u(x, t) of ( $$*$$ ) is globally defined and blows-up in infinite time. As $$t\rightarrow +\infty $$ it has the approximate profile $$\begin{aligned} u(x,t) \approx \frac{1}{\lambda ^2(t)} U\left( \frac{x-\xi (t)}{\lambda (t)} \right) , \quad U(y)= \frac{8}{(1+|y|^2)^2}, \end{aligned}$$ where $$\lambda (t) \approx \frac{c}{\sqrt{\log t}}$$ , $$\xi (t)\rightarrow q$$ for some $$c>0$$ and $$q\in {\mathbb {R}}^2$$ . This result affirmatively answers the nonradial stability conjecture raised in Ghoul and Masmoudi (Commun Pure Appl Math 71:1957–2015, 2018). - 9 April 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 42 (3) , 547-592
Cluster of vortex helices in the incompressible three-dimensional Euler equations
In an inviscid and incompressible fluid in dimension 3 , we prove the existence of several helical filaments, or vortex helices, collapsing into each other.
- 9 April 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Annales de l'Institut Henri Poincaré C, Analyse non linéaire
- Vol. 42 (3) , 547-592
Cluster of vortex helices in the incompressible three-dimensional Euler equations
In an inviscid and incompressible fluid in dimension 3 , we prove the existence of several helical filaments, or vortex helices, collapsing into each other.
- Open Access
Existence of finite time blow-up in Keller-Segel system
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =Δu - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R}^2\times(0,T),\\[5pt] v = (-Δ_{\mathbb{R}^2})^{-1} u := \displaystyle\frac {1}{2π} \displaystyle\int_{\mathbb{R}^2} \log \frac {1}{|x-z|}u(z,t) dz, \ \ \ \ \ \ \ \ \ (\star)\\[5pt] u(\cdot ,0) = u_{0}^{\star} \ge 0 \ \ \ \text{in } \mathbb{R}^2. \end{cases} \end{equation}$ We show that there exists $\varepsilon>0$ such that for any $m$ satisfying $8π<m\le 8π+\varepsilon$ and any $k$ given points $q_{1},...,q_{k}$ in $\mathbb{R}^{2}$ there is an initial data $u_0^*$ of $(\star)$ for which the solution $u(x,t)$ blows-up in finite time as $t\to T$ with the approximate profile $$u(x,t)=\sum_{j=1}^{k}\frac{1}{λ_{j}^{2}(t)}U\left(\frac{x-ξ_{j}(t)}{λ_{j}(t)}\right)(1+o(1)), U(y)=\frac{8}{(1+|y|^{2})^{2}},$$ with $λ_{j}(t) \approx 2e^{-\frac{γ+2}{2}}\sqrt{T-t}e^{-\sqrt{\frac{|\ln(T-t)|}{2}}} $ where $γ=0.57721...$ is the Euler-Mascheroni constant, $ξ_{j}(t)\to q_{j}\in \mathbb{R}^{2}$ and such that $\int_{\mathbb{R}^2}u(x,t)dx=km.$ This construction generalizes the existence result of the stable blow-up dynamics recently proved in \cite{CGMN1,CGMN2}.Open AccessExistence of finite time blow-up in Keller-Segel system
Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =Δu - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R}^2\times(0,T),\\[5pt] v = (-Δ_{\mathbb{R}^2})^{-1} u := \displaystyle\frac {1}{2π} \displaystyle\int_{\mathbb{R}^2} \log \frac {1}{|x-z|}u(z,t) dz, \ \ \ \ \ \ \ \ \ (\star)\\[5pt] u(\cdot ,0) = u_{0}^{\star} \ge 0 \ \ \ \text{in } \mathbb{R}^2. \end{cases} \end{equation}$ We show that there exists $\varepsilon>0$ such that for any $m$ satisfying $8π<m\le 8π+\varepsilon$ and any $k$ given points $q_{1},...,q_{k}$ in $\mathbb{R}^{2}$ there is an initial data $u_0^*$ of $(\star)$ for which the solution $u(x,t)$ blows-up in finite time as $t\to T$ with the approximate profile $$u(x,t)=\sum_{j=1}^{k}\frac{1}{λ_{j}^{2}(t)}U\left(\frac{x-ξ_{j}(t)}{λ_{j}(t)}\right)(1+o(1)), U(y)=\frac{8}{(1+|y|^{2})^{2}},$$ with $λ_{j}(t) \approx 2e^{-\frac{γ+2}{2}}\sqrt{T-t}e^{-\sqrt{\frac{|\ln(T-t)|}{2}}} $ where $γ=0.57721...$ is the Euler-Mascheroni constant, $ξ_{j}(t)\to q_{j}\in \mathbb{R}^{2}$ and such that $\int_{\mathbb{R}^2}u(x,t)dx=km.$ This construction generalizes the existence result of the stable blow-up dynamics recently proved in \cite{CGMN1,CGMN2}. - Open Access
Leapfrogging vortex rings for the 3-dimensional incompressible Euler equations
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid $3$-dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3d Euler equations exhibiting this motion pattern.
Open AccessLeapfrogging vortex rings for the 3-dimensional incompressible Euler equations
A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid $3$-dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3d Euler equations exhibiting this motion pattern.
- Open Access
Cluster of vortex helices in the incompressible $3$d Euler equations
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.
Open AccessCluster of vortex helices in the incompressible $3$d Euler equations
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.