Gevrey Class Smoothing Effect for the Prandtl Equation

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...

Gevrey class regularity for the attractor of the laser equations

Constantin, Foais and Gibbon proved that the laser equations (Lorenz PDE) define a dynamical system in L2 with a C∞ attractor. We extend this theorem to show that the attractor is contained in every Gevrey class, G , for 1 < s < ∞. This demonstrates a remarkable smoothing mechanism for this hyperbolic system. We consider the consequences of this theorem for finitedimensionality of the dynamics....

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.

A Smoothing Technique for the Minimum Norm Solution of Absolute Value Equation

One of the issues that has been considered by the researchers in terms of theory and practice is the problem of finding minimum norm solution. In fact, in general, absolute value equation may have infinitely many solutions. In such cases, the best and most natural choice is the solution with the minimum norm. In this paper, the minimum norm-1 solution of absolute value equation is investigated. ...