Related papers: Global Low Regularity Solutions of Quasi-linear Wa…

Existence of global regular solution branches of the Boltzmann Cauchy problem with continuously differentiable data in phase space dimension $2d\geq 6$ with polynomial decay at infinity of order greater than $2d$ is proved. There are data…

We study the global existence of small data solutions for Cauchy problem for the semi-linear structural damped wave equation with source term.

In this paper, we discuss the Cauchy Problem for the compressible isentropic Euler-Boltzmann equations with vacuum in radiation hydrodynamics. Firstly, we establish the local existence of regular solutions by the fundamental methods in the…

In this paper, we establish global existence of smooth solutions for the Cauchy problem of the critical nonlinear wave equation with time dependent variable coefficients in three space dimensions…

We discuss the Cauchy problem for anisotropic wave equations. Precisely, we address the question to know which kind of Cauchy data on the lateral boundary are necessary to guarantee the uniqueness of continuation of solutions of an…

In this paper, we study the global existence of solutions of the Cauchy problem for a class of weakly dissipative nonlinear dispersive wave equations…

We prove an existence and uniqueness of solution for the Cauchy problem of the simplest nonlinear short-wave equation, $u_{tx}=u-3u^{2}$, with periodic boundary condition.

In this paper, we consider Cauchy problem of simplified Ericksen-Leslie system in dimension three. We establish the unique existence of global smooth solution under some nonlinear conditions on initial data. However, we do not need small…

We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical…

We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of…

We consider the global existence and blow up of solutions of the Cauchy problem of the quasilinear wave equation: $\partial_{t}^2 u = \partial_x(c(u)^2 \partial_x u)$, which has richly physical backgrounds. Under the assumption that…

This paper addresses the Cauchy problem for the cubic defocusing nonlinear Schr\"odinger equation (NLS) with almost periodic initial data. We prove that for small analytic quasiperiodic initial data satisfying Diophantine frequency…

We consider the Cauchy problem for the wave equation in the whole space, R^n, with initial data which are distributions supported on finite sets. The main result is a precise description of the geometry of the sets of stationary points of…

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…

In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is…

We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…

After recalling basic features of the theory of symmetric quasi regular Dirichlet forms we show how by applying it to the stochastic quantization equation, with Gaussian space-time noise, one obtains weak solutions in a large invariant set.…

This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…

In this paper, we consider the Cauchy problem of the two-dimensional regularized incompressible magnetohydrodynamics equations. The main objective of this paper is to establish the global regularity of classical solutions of the…

For any bounded smooth domain $\Omega\subset\mathbb R^3$, we establish the global existence of a weak solution $u:\Omega\times (0,+\infty)\to\mathbb R^3\times\mathbb S^2$ of the initial-boundary value (or the Cauchy) problem of the…