Vanishing viscosity limit of navier-stokes equations in gevrey class

Feng Cheng (1) , Wei-Xi Li (1) , Chao-Jiang Xu (2)

1 School of Mathematics and Statistics [Wuhan University]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

In this paper we consider the inviscid limit for the periodic solutions to Navier-Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier-Stokes equation is independent of viscosity, and that the solutions of the Navier-Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover the convergence rate in Gevrey class is presented.

Mots clés: Gevrey class; Incompressible Navier Stokes equation; Vanishing viscosity limi

Domaines: Equations aux dérivées partielles [math.AP]

Feng Cheng, Wei-Xi Li, Chao-Jiang Xu. Vanishing viscosity limit of navier-stokes equations in gevrey class. 2017. ⟨hal-01473694⟩