34 citations · 42 across the 19 of their papers we have counts for
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Global strong solutions to the compressible Navier-Stokes system with potential temperature transport
Xiaoping Zhai, Yongsheng Li, Fujun Zhou
We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in Different from the Navier-Stokes-Fourier syste…
Global well-posedness and inviscid limits of the generalized Oldroyd type models
Xiaoping Zhai, Yuanyuan Dan, Yongsheng Li
We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in . Our result give positive answers partially to the qu…
Global small solutions to the inviscid Hall-MHD system
Xiaoping Zhai, Yongsheng Li, Yajuan Zhao
The local existence of smooth solutions to the inviscid Hall-MHD system has been obtained since Chae, Degond and Liu [Ann. Inst. H. Poincaré Anal. Non Linéaire, {31} (2014), 555--5…
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li +1
We consider the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili (RMKP) equation \begin{align*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\partial_{x}(u^{2})\right…
Probabilistic pointwise convergence problem of some dispersive equations
Wei Yan, Jinqiao Duan, Yongsheng Li +1
In this paper, we investigate the almost surely pointwise convergence problem of free KdV equation, free wave equation, free elliptic and non-elliptic Schrödinger equation respecti…
Global wellposedness and large time behavior of solutions to the -dimensional compressible Oldroyd-B model
Xiaoping Zhai, Yongsheng Li
The purpose of this work is to study the global wellposedness and large time behavior results of strong solutions for the compressible Oldroyd-B model derived by Barrett, Lu, Süli…
Global well-posedness of the Cauchy problem for a fifth-order KP-I equation in anisotropic Sobolev spaces
Yongsheng Li, Wei Yan, Yimin Zhang
In this paper, we consider the Cauchy problem for the fifth-order KP-I equation \begin{align*} u_t + \partial_x^5u+\partial_x^{-1}\partial_y^2u + \frac{1}{2}\partial_x(u^2)=0. \end…
The Cauchy problem for two dimensional generalized Kadomtsev-Petviashvili-I equation in anisotropic Sobolev spaces
Wei Yan, Yongsheng Li, Jianhua Huang +1
The goal of this paper is three-fold. Firstly, we prove that the Cauchy problem for generalized KP-I equation \begin{eqnarray*} u_{t}+|D_{x}|^α\partial_{x}u+\partial_{x}^{-1}\parti…
Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces
Wei Yan, Yongsheng Li, Yimin Zhang
In this paper, we consider the Cauchy problem for the generalized KP-II equation \begin{eqnarray*} u_{t}-|D_{x}|^αu_{x}+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u…
Random data Cauchy problem for the wave equation on compact manifold
Jinqiao Duan, Jianhua Huang, Yongsheng Li +1
Inspired by the work of Burq and Tzvetkov (Invent. math. 173(2008), 449-475.), firstly, we construct the local strong solution to the cubic nonlinear wave equation with random data…
The Cauchy problem for higher-order modified Camassa-Holm equations on the circle
Wei Yan, Yongsheng Li, Xiaoping Zhai +1
In this paper, we investigate the Cauchy problem for the shallow water type equation \begin{eqnarray*} u_{t}+\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2})+ \partial_{x}(1-\…
Sharp well-posedness and ill-posedness of the Cauchy problem for the higher-order KdV
Wei Yan, Minjie Jiang, Yongsheng Li +1
In this paper, we investigate the Cauchy problem for the higher-order KdV-type equation \begin{eqnarray*} u_{t}+(-1)^{j+1}\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2}) = 0,…
On the Well-posedness of 2-D Incompressible Navier-Stokes Equations with Variable Viscosity in Critical Spaces
Huan Xu, Yongsheng Li, Xiaoping Zhai
In this paper, we first prove the local well-posedness of the 2-D incompressible Navier-Stokes equations with variable viscosity in critical Besov spaces with negative regularity i…
The Cauchy problem for a higher order shallow water type equation on the circle
Wei Yan, Yongsheng Li, Jianhua Huang
In this paper, we investigate the Cauchy problem for a higher order shallow water type equation \begin{eqnarray*} u_{t}-u_{txx}+\partial_{x}^{2j+1}u-\partial_{x}^{2j+3}u+3uu_{x}-2u…
Global well-posedness for the 3-D density-dependent liquid crystal flows in the critical Besov spaces
Xiaoping Zhai, Yongsheng Li, Wei Yan
In this paper, we prove the local well-posedness of 3-D density-dependent liquid crystal flows with initial data in the critical Besov spaces, without assumptions of small density…
The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
Yongsheng Li, Jianhua Huang, Wei Yan
In this paper, we investigate the Cauchy problem for the Ostrovsky equation \begin{eqnarray*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\frac{1}{2}\partial_{x}(u^{2})\right) -γu=…
Global Attractor for Weakly Damped Forced KdV Equation in Low Regularity on T
Yongsheng Li, Yifei Wu
In this paper we consider the long time behavior of the weakly damped, forced Korteweg-de Vries equation in the Sololev spaces of the negative indices in the periodic case. We prov…
On a quadratic nonlinear Schrödinger equation: sharp well-posedness and ill-posedness
Yongsheng Li, Yifei Wu
We study the initial value problem of the quadratic nonlinear Schrödinger equation where $u:\R\times \R\to \C$. We prove that it's locally well-posed in…
Global well-posedness for the Benjamin equation in low regularity
Yongsheng Li, Yifei Wu
In this paper we consider the initial value problem of the Benjamin equation where $u:\R\times [0,T]\map…