Related papers: Global solution in critical spaces to the compress…
In this paper, we are concerned with the three-dimensional nonhomogeneous B\'enard system with density-dependent viscosity in bounded domain. The global well-posedness of strong solution is established, provided that the initial total mass…
We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively…
In this paper we prove global well-posedness and modified scattering for the massive Maxwell-Klein-Gordon equation in the Coulomb gauge on $\mathbb{R}^{1+d}$ $(d \geq 4)$ for data with small critical Sobolev norm. This extends to the…
In this paper, we mainly study the Cauchy problem for the full compressible Navier-Stokes equations in Sobolev spaces. We establish the global well-posedness of the equations with small initial data by using Friedrich's method and…
We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the…
In this paper we prove that the cubic wave equation is globally well - posed and scattering for radial initial data lying in $B_{1,1}^{2} \times B_{1,1}^{1}$. This space of functions is a scale invariant subspace of $\dot{H}^{1/2} \times…
We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…
We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Our construction starts with the existence of solution to the truncated subcritical problem.…
The Cauchy problem for the Kadomtsev-Petviashvili-II equation (u_t+u_{xxx}+uu_x)_x+u_{yy}=0 is considered. A small data global well-posedness and scattering result in the scale invariant, non-isotropic, homogeneous Sobolev space \dot…
The Cauchy problem for the 1-dimensional Zakharov system is shown to be globally well-posed for large data which not necessarily have finite energy. The proof combines the local well-posedness result of Ginibre, Tsutsumi, Velo and a general…
In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies…
We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with…
In this article, we prove the global well-posedness and scattering of the cubic focusing infinite coupled nonlinear Schr\"odinger system on $\mathbb{R}^2$ below the threshold in $L_x^2h^1(\mathbb{R}^2\times \mathbb{Z})$. We first establish…
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 variation. Furthermore, if the initial density is close…
This paper is dedicated to the Oldroyd-B model with fractional dissipation $(-\Delta)^{\alpha}\tau$ for any $\alpha>0$. We establish the global smooth solutions to the Oldroyd-B model in the corotational case with arbitrarily small…
In this paper, we study the global well-posedness and decay rates of strong solutions to an incompressible Vlasov-MHD model arising in magnetized plasmas. This model is consist of the Vlasov equation and the incompressible…
In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the characteristics of the dispersion equation, we make…
The L^2 -critical defocusing nonlinear Schrodinger initial value problem on R^d is known to be locally well-posed for initial data in L^2. Hamiltonian conservation and the pseudoconformal transformation show that global well-posedness holds…