Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption

Gevrey Class Smoothing Effect for the Prandtl Equation

Global Gevrey Regularity for the B Enard Convection in Porous Medium with Zero Darcy-prandtl Number

In this paper, we prove the existence and uniqueness for the three-dimensional B enard convection model in porous medium with zero Darcy-Prandtl number using the Galerkin procedure. In addition, we show that the solutions to this problem are analytic in time with values in a Gevrey class regularity. We also prove that the solution of the standard Galerkin method converges exponentially fast, in...

Wellposedness of the tornado-hurricane equations

We prove local-in-time existence of a unique mild solution for the tornado-hurricane equations in a Hilbert space setting. The wellposedness is shown simultaneously in a halfspace, a layer, and a cylinder and for various types of boundary conditions which admit discontinuities at the edges of the cylinder. By an approach based on symmetric forms we first prove maximal regularity for a linearize...

Some Local Wellposedness Results for Nonlinear Schrödinger Equations below L

In this paper we prove some local (in time) wellposedness results for non-linear Schrödinger equations ut − i∆u = N (u, u), u(0) = u0 with rough data, that is, the initial value u0 belongs to some Sobolev space of negative index. We obtain positive results for the following nonlinearities and data:

The Gevrey hypoellipticity for a class of kinetic equations

In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.