Related papers: Global smooth solutions to 2D semilinear wave equa…

The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was…

In this paper, we establish the global existence of smooth solutions of the three-dimensional MHD system for a class of large initial data. Both the initial velocity and magnetic field can be arbitrarily large in the critical norm.

We are interested in studying the coupled wave and Klein-Gordon equations with null quadratic nonlinearities in $\mathbb{R}^{2+1}$. We want to establish the small data global existence result, and in addition, we also demonstrate the…

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 discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…

We are interested in the cubic Dirac equation in two space dimensions. We establish the small data global existence and sharp pointwise decay results for general cubic nonlinearities without additional structure. We also prove the…

We construct oscillatory solutions of fully semilinear wave equations in Minkowski space satisfying a null condition of the form $$\square u:=(-\partial_{x_0}^2 +\sum_{j=1}^n \partial_{x_j}^2 )u=…

This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay…

In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite…

This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa,…

We consider the two-dimensional quasilinear wave equations with standard null-form type quadratic nonlinearities. We prove global wellposedness without using the Lorentz boost vector fields.

In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term.…

We prove the existence of global solutions to the focusing energy-supercritical semilinear wave equation in R^{3+1} for arbitrary outgoing large initial data, after we modify the equation by projecting the nonlinearity on outgoing states.

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

We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but possibly large oscillations where the initial…

We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the…

We consider the quadratically semilinear wave equation on R^d, d>=3, equipped with a Riemannian metric. This metric is non-trapping and approaches the Euclidean metric polynomially at infinity. Using Mourre estimates and the Kato theory of…

We study the propagation of a compactly supported high-frequency wave through a semi-linear wave equation with a null structure. We prove that the self-interaction of the wave creates harmonics which remain close to the light-cone in the…

In 1871, Saint-Venant introduced the renowned shallow water equations. Since then, for the two-dimensional viscous or inviscid shallow water equations, the global existence of smooth solutions with arbitrarily large initial data has…

We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…