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The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic…
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric fluid under the additional assumption that it is incompressible and stratified. In this setting we show that the…
We study the stabilities and classical solutions of Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. In fact, we extend the study the stabilities of Euler-Poisson equations with or without frictional…
We study the Cauchy problem for 3-D nonlinear elastic waves satisfying the null condition with low regularity initial data. In the radially symmetric case, we prove the global existence of a low regularity solution for every small data in…
In this paper, the finite time blow-up of smooth solutions to the Cauchy problem for full Euler-Poisson equations and isentropic Euler-Poisson equations with repulsive forces or attractive forces in high dimensions $(n\geq3)$ is proved for…
We prove the existence of time-quasi-periodic solutions of the incompressible Euler equation on the three-dimensional torus $\T^3$, with a small time-quasi-periodic external force. The solutions are perturbations of constant (Diophantine)…
The three-dimensional quasi-geostrophic equation is considered over a cylindrical domain with a multiply connected horizontal cross-section. Homogeneous Neumann boundary conditions, tantamount to homogeneous density fields, are imposed on…
We study systems interpolating between the 3D incompressible Euler and electron--MHD equations, given by \begin{equation*} \partial_t B + V \cdot \nabla B = B\cdot \nabla V, \qquad V = -\nabla\times (-\Delta)^{-a} B, \qquad \nabla\cdot B =…
In this result, we develop the techniques of \cite{KS1} and \cite{BW} in order to determine a class of stable perturbations for a minimal mass soliton solution of a saturated, focusing nonlinear Schr\"odinger equation {c} i u_t + \Delta u +…
We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge…
In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in $\mathbb{R}^3$. We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of…
We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete. For…
This paper investigates the stabilization effect of a background magnetic vorticity on electrically conducting fluids. By exploring the dissipation nature of the linearized equations, we prove the global existence of smooth solutions to the…
We prove a stability result of constant equilibria for the three-dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity…
We demonstrate that neutral Dirac particles in external electric fields, which are equivalent to generalized Dirac oscillators, are physical examples of quasi-exactly solvable systems. Electric field configurations permitting quasi-exact…
In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…
In this paper, we are concerned with the global existence and blowup of smooth solutions of the 3-D compressible Euler equation with time-depending damping $$ \partial_t\rho+\operatorname{div}(\rho u)=0, \quad \partial_t(\rho…
The initial boundary value problems for compressible Navier-Stokes-Poisson is considered on a bounded domain in $\mathbb{R}^3$ in this paper. The global existence of smooth solutions near a given steady state for compressible…
We study global behavior of small solutions of the Gross-Pitaevskii equation in three dimensions. We prove that disturbances from the constant equilibrium with small, localized energy, disperse for large time, according to the linearized…
This work is concerned with the global existence of large solutions to the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible…