相关论文: Stability of vacuum for the Landau equation with h…
We first establish existence for all positive time near equilibrium for the moving interface problem between the Navier-Stokes equations for the evolving fluid phase (moved by the fluid velocity) and an elastic body modelled by the linear…
In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L2…
In this paper, we prove the global existence of smooth solutions to the three-dimensional incompressible magneto-hydrodynamical system with initial data close enough to the equilibrium state, $(e_3,0).$ Compared with the the previous works…
We study the nonlinear stability of the $(3+1)$-dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of cosmological black holes, we construct the solution of the…
We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to…
Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step is to…
We study the regular sets of local energy solutions to the Navier-Stokes equations in terms of conditions on the initial data. It is shown that if a weighted $L^2$ norm of the initial data is finite, then all local energy solutions are…
In this document we discuss the long time behaviour for the homogeneous Landau-Fermi-Dirac equation in the hard potential case. Uniform in time estimates for statistical moments and Sobolev regularity are presented and used to prove…
We investigate the global stability and non-vanishing vacuum states of large solutions to the compressible Navier-Stokes equations on the torus $\mathbb{T}^3$, and the main novelty of this work is three-fold: First, under the assumption…
We give a new proof of the global stability of Minkowski space originally established in the vacuum case by Christodoulou and Klainerman. The new approach shows that the Einstein-vacuum and the Einstein-scalar field equations with general…
In this paper we study the Boltzmann equation near global Maxwellians in the $d$-dimensional whole space. A unique global-in-time mild solution to the Cauchy problem of the equation is established in a Chemin-Lerner type space with respect…
We study the Cauchy problem for the quasilinear wave equation $ \partial^2 _t u = u^{2a} \partial^2_x u + F(u) u_x $ with $a \geq 0$ and show a result for the local in time existence under new conditions. In the previous results, it is…
The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…
In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is…
In this article, we prove the existence of global weak solutions to the three-dimensional focusing energy-critical nonlinear Schr\"odinger (NLS) equation in the non-radial case. Furthermore, we prove the weak-strong uniqueness for some…
The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\infty_xL^1_{v}\cap L^\infty_{x,v}$ approach, we prove the global…
We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…
We present in this document some essential properties of solutions to the homogeneous Landau-Fermi-Dirac equation for moderately soft potentials. Uniform in time estimates for statistical moments, $L^{p}$-norm generation and Sobolev…
We investigate in this work the rate of convergence to equilibrium of solutions to the spatially homogeneous Landau equation with soft potentials. Firstly, we prove a polynomial in time convergence using an entropy method with some new a…
First of all, we get the global existence of classical and strong solutions of the full compressible Navier-Stokes equations in three space dimensions with initial data which is large and spherically or cylindrically symmetric. The…