相关论文: Landau damping for analytic and Gevrey data

In this paper, we study Landau damping in the weakly collisional limit of a Vlasov-Fokker-Planck equation with nonlinear collisions in the phase-space $(x,v) \in \mathbb T_x^n \times \mathbb R^n_v$. The goal is four-fold: (A) to understand…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Our last three papers provide an occasion to make some brief notes on ideology of waves in plasmas and to rehabilitate Vlasov prescription to calculate relevant logarithmically divergent integrals in the principal value sense. In this…

In this paper, we study the Landau equation under the Navier-Stokes scaling in the torus for hard and moderately soft potentials. More precisely, we investigate the Cauchy theory in a perturbative framework and establish some new short time…

We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the…

We obtain rigorous large time asymptotics for the Landau-Lifshitz equation in the soliton free case by extending the nonlinear steepest descent method to genus 1 surfaces. The methods presented in this paper pave the way to a rigorous…

We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…

We study the problem of solving fixed-point equations for seminorm-contractive operators and establish foundational results on the non-asymptotic behavior of iterative algorithms in both deterministic and stochastic settings. Specifically,…

The mechanism of Landau damping is observed in various systems from plasma oscillations to accelerators. Despite its widespread use, some confusion has been created, partly because of the different mechanisms producing the damping but also…

We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…

We prove a new invariant torus theorem, for $\alpha$-Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the $\alpha$-Bruno-R\"ussmann condition, and which reduces to the classical Bruno-R\"ussmann condition in…

We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave…

We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus $\mathbb T^3$ of the prototype \begin{align*} &u_{tt}-\Delta…

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational…

We perform a well defined derivative expansion to obtain the time dependent effective theory for a BCS superconductor at finite temperature, using an arbitrary curve in the complex time plane. Our expansion is unique, being free of any…

We consider nonlinear solvers for the incompressible, steady (or at a fixed time step for unsteady) Navier-Stokes equations in the setting where partial measurement data of the solution is available. The measurement data is…

We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Comm. Math. Sci. 6, 749-764 (2008) following the work in…

We study the asymptotic behavior of small data solutions to the screened Vlasov Poisson(i.e. Vlasov-Yukawa) equation on ${\mathbb R}\times{\mathbb R}$ near vacuum. We show that for initial data small in Gevrey-2 regularity, the derivative…

The deterministic inviscid primitive equations (also called the hydrostatic Euler equations) are known to be ill-posed in Sobolev spaces and in Gevrey classes of order strictly greater than 1, and some of their analytic solutions exist only…