Related papers: Global rough solutions for the Zakharov system in …
We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result…
We study the Cauchy problem for the Zakharov system in spatial dimension $d\ge 4$ with initial datum $(u(0), n(0), \partial_t n(0)) \in H^k(\mathbb{R}^d) \times \dot{H}^l(\mathbb{R}^d)\times \dot{H}^{l-1}(\mathbb{R}^d)$. According to…
We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We…
In this paper we prove global well-posedness and scattering for the conformal, defocusing, nonlinear wave equation with radial initial data in the critical Sobolev space, for dimensions $d \geq 4$. This result extends a previous result…
We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\geq 2$. We introduce a new notion of \textit{quasi-solutions} when the initial velocity is assumed to…
We consider two-dimensional quasilinear wave equations with standard null-type quadratic nonlinearities. In 2001 Alinhac proved that such systems possess global in time solutions for compactly supported initial data with sufficiently small…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
We prove global existence and modified scattering property for the solutions of the $2D$ gravity water waves system in the infinite depth setting for a class of initial data, which is only required to be small above the level…
We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…
We consider a class of wave-Schroedinger systems with a Zakharov-Schulman type coupling. This class of systems is indexed by a parameter gamma which measures the strength of the null form in the nonlinearity of the wave equation. The case…
We obtain a global existence result for the three-dimensional Navier-Stokes equations with a large class of initial data allowing growth at spatial infinity. Our work is a continuation of the results by T.-P. Tsai, Z. Bradshaw, I. Kukavica…
This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces $H^k(\mathbb R^d)\!\times\!H^l(\mathbb R^d)\!\times\!H^{l-1}\!(\mathbb R^d)$. We recall the well-posedness and ill-posedness results…
In dimensions greater than or equal to 3, we prove that the Schroedinger map initial-value problem is globally well-posed for small data in the critical Besov space.
Assuming initial data have small weighted $H^4\times H^3$ norm, we prove global existence of solutions to the Cauchy problem for systems of quasi-linear wave equations in three space dimensions satisfying the null condition of Klainerman.…
In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…
This paper studies the regularity of solutions to the Zakharov and Klein-Gordon-Schr\"{o}dinger systems at low regularity levels. The main result is that the nonlinear part of the solution flow falls in a smoother space than the initial…
We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.
We prove that the Cauchy problem for the two-dimensional Zakharov system is locally well-posed for initial data which are localized perturbations of a line solitary wave. Furthermore, for this Zakharov system, we prove weak convergence to a…
As a continuation of the previous work \cite{Wu}, we consider the global well-posedness for the derivative nonlinear Schr\"odinger equation. We prove that it is globally well-posed in energy space, provided that the initial data $u_0\in…
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…