相关论文: Global well-posedness for the Gross-Pitaevskii equ…

In this paper, we establish the global well-posedness of the Cauchy problem for the Gross-Pitaevskii equation with an angular momentum rotational term in which the angular velocity is equal to the isotropic trapping frequency in the space…

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 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{align*} Firstly, we establish the local well-posedness of…

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…

In this paper, we consider the Cauchy problem for the generalized KP-II equation \begin{eqnarray*} u_{t}-|D_{x}|^{\alpha}u_{x}+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u^{2})=0,\alpha\geq4. \end{eqnarray*} The goal of this…

This paper is concerned with the Cauchy problem of the $2$D Zakharov-Kuznetsov equation. We prove bilinear estimates which imply local in time well-posedness in the Sobolev space $H^s({\mathbb{R}}^2)$ for $s > -1/4$, and these are optimal…

We establish local and global well-posedness for the Cauchy problem of a generalized Camassa-Holm equation where orders of the momentum and the nonlinearity can be arbitrarily high. More precisely, we consider the equation \begin{equation*}…

In this paper, we study the Cauchy problem of the Euler-Nernst-Planck-Possion system. We obtain global well-posedness for the system in dimension $d=2$ for any initial data in $H^{s_1}(\mathbb{R}^2)\times H^{s_2}(\mathbb{R}^2)\times…

As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole space is proved in some suitable weighted Sobolev spaces…

We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global…

This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in…

In this work we prove local and global well-posedness results for the Cauchy problem of a family of regularized nonlinear Benjamin-type equations in both periodic and nonperiodic Sobolev spaces.

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the…

We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain…

The Cauchy problem for the Chern-Simons-Higgs system in the (2+1)-dimensional Minkowski space in temporal gauge is globally well-posed in energy space improving a result of Huh. The proof uses the bilinear space-time estimates in…

We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical Besov spaces, which generalize the result in [10]. Meanwhile , we analyze the…

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…

We prove that the Cauchy problem for the 2D quintic defocusing biharmonic Schr\"odinger equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{R}^2)$ for $\frac{8}{7}<s<2$. Our main ingredient to establish the result is the…

The I-method in its first version as developed by Colliander et al. is applied to prove that the Cauchy-problem for the generalised Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the…

The Cauchy problem of the Cahn-Hilliard equations is studied in three-dimensional space. Firstly, we construct its approximate fourth-order parabolic equation, obtaining the existence of solutions by the Aubin-Lions's compactness lemma.…