Related papers: Long-time dynamics for the Kelvin-Helmholtz equati…
We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved…
This paper is concerned with global existence as well as infinite-time blowups of classical solutions to the following fully parabolic kinetic system \begin{equation} \begin{cases} u_t=\Delta (\gamma (v)u) v_t-\Delta v+v=u \end{cases}…
We revisit the problem of stationary distribution of vorticity in three-dimensional turbulence. Using Clebsch variables we construct an explicit invariant measure on stationary solutions of Euler equations with the extra condition of fixed…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
We study the linear theory of Kelvin-Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations…
We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $\theta \in (0,\pi)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized…
The 1-D Two-Fluid Model (TFM) promises a powerful and computationally cheap platform for simulating multi-fluid flow phenomena. However, runaway Kelvin-Helmholtz instabilities plagued previous approaches, necessitating aphysical…
We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the…
In this paper, we consider exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove global existence of smooth solutions. Similar to the constant coefficients case, we show…
We study well-posedness and long-time dynamics of a class of quasilinear wave equations with a strong damping. We accept the Kirchhoff hypotheses and assume that the stiffness and damping coefficients are $C^1$ functions of the $L_2$-norm…
We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of ${\mathbb {R}}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state…
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by…
In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…
In the present work, we consider a variety of two-component, one-dimensional states in nonlinear Schrodinger equations in the presence of a parabolic trap, inspired by the atomic physics context of Bose-Einstein condensates. The use of…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
We study the linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold. In particular we prove that these equations are linearization stable in the neighborhood of vacuum solutions for a…
We prove an abstract infinite dimensional KAM theorem, which could be applied to prove the existence and linear stability of small-amplitude quasi-periodic solutions for one dimensional forced Kirchhoff equations with periodic boundary…
We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is…
The Vicsek-BGK equation is a kinetic model for alignment of particles moving with constant speed between stochastic reorientation events with sampling from a von Mises distribution. The spatially homogeneous model shows a steady state…
As one of the cornerstones of fluid mechanics, stability analyses provide essential physical insights into the growth of perturbations and eventual transition to turbulence. However, classical \enquote{frozen-time} stability analyses…