Xingyu Li
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Xingyu Li has a total of 5 co-authors. Here are the top co-authors by number of shared publications:
- Arghir Zarnescu
Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao, Bizkaia, Spain
4 shared publications - Marius Paicu
Université Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France
3 shared publications - Chuqi Cao
Department of Mathematics The Chinese University of Hong Kong P. R. China
1 shared publication - Dingqun Deng1 shared publication
- Francesco De Anna
Institute of Mathematics University of Würzburg
1 shared publication
Latest Publications
- Open Access
On hydrostatic limit of Beris-Edwards system in a thin strip
In this paper we consider the 3D co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in a thin strip. The system contains the incompressible Navier-Stokes, coupled with a parabolic system for matrix-valued functions, the $Q$-tensors. We show that under a suitable scaling, corresponding, in the Navier-Stokes part, to the hydrostatic scaling, one obtains in the limit a partly decoupled system. For the fluid part we obtain the Prandtl system while for the $Q$-tensors we obtain a non-standard system, involving fluids components and a non-standard combination of partly dissipative equations and algebraic constraints. We prove the convergence of the rescaled system and the well-posedness of the limit in Sobolev spaces.
Open AccessOn hydrostatic limit of Beris-Edwards system in a thin strip
In this paper we consider the 3D co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in a thin strip. The system contains the incompressible Navier-Stokes, coupled with a parabolic system for matrix-valued functions, the $Q$-tensors. We show that under a suitable scaling, corresponding, in the Navier-Stokes part, to the hydrostatic scaling, one obtains in the limit a partly decoupled system. For the fluid part we obtain the Prandtl system while for the $Q$-tensors we obtain a non-standard system, involving fluids components and a non-standard combination of partly dissipative equations and algebraic constraints. We prove the convergence of the rescaled system and the well-posedness of the limit in Sobolev spaces.
- 1 January 2024
- Published by International Press of Boston in Communications in Mathematical Sciences
- Vol. 22 (6) , 1701-1732
The hydrostatic limit of the Beris-Edwards system in dimension two
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2024
- Published by International Press of Boston in Communications in Mathematical Sciences
- Vol. 22 (6) , 1701-1732
The hydrostatic limit of the Beris-Edwards system in dimension two
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- Open Access
The Vlasov-Maxwell-Boltzmann/Landau system with polynomial perturbation near Maxwellian
In this paper, we study the Vlasov-Maxwell-Boltzmann system without angular cutoff and the Vlasov-Maxwell-Landau/Boltzmann system with polynomial perturbation $F=μ+f$ near global Maxwellian. In particular, we prove the global existence, uniqueness and large time behavior for solutions in a polynomial weighted space $H^N_{x,v}(\langle v\rangle^k)$. The method is based on Duhamel's principle with the crucial time-decay analysis on the particle distribution $f$ and the electromagnetic field $(E,B)$.Open AccessThe Vlasov-Maxwell-Boltzmann/Landau system with polynomial perturbation near Maxwellian
In this paper, we study the Vlasov-Maxwell-Boltzmann system without angular cutoff and the Vlasov-Maxwell-Landau/Boltzmann system with polynomial perturbation $F=μ+f$ near global Maxwellian. In particular, we prove the global existence, uniqueness and large time behavior for solutions in a polynomial weighted space $H^N_{x,v}(\langle v\rangle^k)$. The method is based on Duhamel's principle with the crucial time-decay analysis on the particle distribution $f$ and the electromagnetic field $(E,B)$. - Open Access
Patterns in a Smoluchowski Equation
We analyze the dynamics of concentrated polymer solutions modeled by a 2D Smoluchowski equation. We describe the long time behavior of the polymer suspensions in a fluid. \par When the flow influence is neglected the equation has a gradient structure. The presence of a simple flow introduces significant structural changes in the dynamics. We study the case of an externally imposed flow with homogeneous gradient. We show that the equation is still dissipative but new phenomena appear. The dynamics depend on both the concentration intensity and the structure of the flow. In certain {\it limit cases} the equation has a gradient structure, in an appropriate reference frame, and the solutions evolve to either a steady state or a tumbling wave. For small perturbations of the gradient structure we show that some features of the gradient dynamics survive: for small concentrations the solutions evolve in the long time limit to a steady state and for high concentrations there is a tumbling wave.
Open AccessPatterns in a Smoluchowski Equation
We analyze the dynamics of concentrated polymer solutions modeled by a 2D Smoluchowski equation. We describe the long time behavior of the polymer suspensions in a fluid. \par When the flow influence is neglected the equation has a gradient structure. The presence of a simple flow introduces significant structural changes in the dynamics. We study the case of an externally imposed flow with homogeneous gradient. We show that the equation is still dissipative but new phenomena appear. The dynamics depend on both the concentration intensity and the structure of the flow. In certain {\it limit cases} the equation has a gradient structure, in an appropriate reference frame, and the solutions evolve to either a steady state or a tumbling wave. For small perturbations of the gradient structure we show that some features of the gradient dynamics survive: for small concentrations the solutions evolve in the long time limit to a steady state and for high concentrations there is a tumbling wave.
- Open Access
The hydrostatic limit of the Beris-Edwards system in dimension two
We study the scaled anisotropic co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in dimension two. We prove the global well-posedness with small analytic data in a thin strip domain. Moreover, we justify the limit to a system involving the hydrostatic Navier-Stokes system with analytic data and prove the convergence.
Open AccessThe hydrostatic limit of the Beris-Edwards system in dimension two
We study the scaled anisotropic co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in dimension two. We prove the global well-posedness with small analytic data in a thin strip domain. Moreover, we justify the limit to a system involving the hydrostatic Navier-Stokes system with analytic data and prove the convergence.