Related papers: Large data global regularity for the $2+1$-dimensi…
In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier--Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates…
For any subcritical index of regularity $s>3/2$, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space…
In this paper, we prove global well-posedness with large initial data for the one-dimensional quasilinear wave equation $$ u_{tt}=c(u)^2u_{xx}, \qquad (t,x)\in (0,T)\times\R, $$ where \(c\) is a positive, bounded, monotonically increasing…
We show that in dimensions $n \geq 6$ that one has global regularity for the Maxwell-Klein-Gordon equations in the Coulomb gauge provided that the critical Sobolev norm $\dot H^{n/2-1} \times \dot H^{n/2-2}$ of the initial data is…
We show that the $3D$ relativistic Vlasov-Maxwell system admits global solution for a class of arbitrarily large cylindrically symmetric initial data.
We prove global existence of the $3D$ relativistic Vlasov-Maxwell system for a class of arbitrary large regular initial data with spherical symmetry, in which the initial distribution function of particles is assumed to decay fast but…
The Cauchy problem for the Gross-Pitaevskii equation in three space dimensions is shown to have an unconditionally unique global solution for data of the form 1 + H^s for 5/6 < s < 1, which do not have necessarily finite energy. The proof…
We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space $H^s$…
We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space $H^{3}(\mathbb{R})\cap H^{2,1}(\mathbb{R})$.This result removes all spectral restrictions on the initial data…
We show an improved global well-posedness result for the Zakharov system in two space dimensions with minimal regularity assumptions for the data. Especially we are able to allow Schroedinger and wave data, which do not belong to H^1 and…
An initial-boundary value problem for the 3D Zakharov-Kuznetsov equation posed on bounded domains is considered. Existence and uniqueness of a global regular solution as well as exponential decay of the $H^2$-norm for small initial data are…
We show that wave maps from Minkowski space $R^{1+n}$ to a sphere are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space $\dot H^{n/2}$ in the high dimensional case $n \geq 5$. A major difficulty,…
There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval $[0,1] \subset \mathbb R$, but little is known about the multidimensional situation. This article tries…
We prove large-data local stability theorems for several spin models in two dimensions.
Given any smooth, suitably small initial data, which decays polynomially at infinity, we prove global regularity for the $3D$ relativistic massive Vlasov-Maxwell system. In particular, the compact support assumption, which is widely used in…
In this paper, we study the global regularity problem for the 2D Rayleigh-B\'{e}nard equations with logarithmic supercritical dissipation. By exploiting a combined quantity of the system, the technique of Littlewood-Paley decomposition and…
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…
We consider the initial value problem for the 2D quasi-geostrophic equation with weak dissipation term $\kappa(-\Delta)^{\alpha/2}\theta\ (0<\alpha\leqslant 1)$ and dispersive forcing term $Au_2$. We establish a unique global solution for a…
We address the well-posedness for the two-dimensional Boussinesq equations with zero diffusivity in bounded domains. We prove global in time regularity for rough initial data: both the initial velocity and temperature have $\epsilon$…
The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schr\"odinger part is small enough. The proof uses a refined I-method originally initiated by Colliander,…