Related papers: Small data global existence and decay for two dime…
Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e. sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The…
We use a novel physical space method to prove relatively non-degenerate integrated energy estimates for the wave equation on subextremal Schwarzschild-de Sitter spacetimes with parameters $(M,\Lambda)$. These are integrated decay statements…
We study the global existence and decay estimates for nonlinear wave equations with the space-time dependent dissipative term in an exterior domain. The linear dissipative effect may vanish in a compact space region. Moreover the nonlinear…
We prove the pointwise decay of solutions to three linear equations: (i) the transport equation in phase space generalizing the classical Vlasov equation, (ii) the linear Schrodinger equation, (iii) the Airy (linear KdV) equation. The usual…
In this paper, we consider the derivative nonlinear Schr\"odinger (DNLS) equation. While the existence theory has been intensely studied, properties like dispersive estimates for the solutions have not yet been investigated. Here we address…
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data solutions to this system in the case of a massive scalar field…
The purpose of this paper is to show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small…
This paper is devoted to several small data existence results for semi-linear wave equations on negatively curved Riemannian manifolds. We provide a simple and geometric proof of small data global existence for any power $p\in (1,…
Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi: \mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the…
We consider the following half wave Schr{\"o}dinger equation,$$\left(i \partial_{t}+\partial_{x }^2-\left|D_{y}\right|\right) U=|U|^{2} U$$on the plane $\mathbb{R}_x \times \mathbb{R}_y$. We prove the existence of modified wave operators…
This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant…
We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a…
In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the…
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 this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
We establish global existence and decay of solutions of a viscous half Klein-Gordon equation with a quadratic nonlinearity considering initial data, whose Fourier transform is small in L1 cap Linfty. Our analysis relies on the observation…
We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…
In this work we establish a weighted $L^2-L^2$ estimate for inhomogeneous wave equation in 3-D, by introducing a Morawetz multiplier with weight of power $s(1<s<2)$, and then integrating on the light cones and $t$ slice. With this weighted…
This article is devoted to a general class of one dimensional NLS problems with a cubic nonlinearity. The question of obtaining scattering, global in time solutions for such problems has attracted a lot of attention in recent years, and…
By using the Strichartz esitmate and Picard iteration, we prove the subcritical(critical in some cases) global solution in $C_t H_x^s\cap C_t^1 H^{s-1}_x$ with small data for semilinear wave equation with nonlinearity of type $(\partial…