Navier–Stokes Equations and Weighted Convolution Inequalities in Groups
Animikh Biswas, David Michael Swanson · Communications in Partial Differential Equations · 2010
We obtain Gevrey regular mild solutions to the incompressible Navier–Stokes equations in R n with periodic boundary condition in a subset of the variables. The method is based on an extension of Young's convolution inequality in weighted Lebesgue spaces of measurable functions defined on locally compact abelian groups. This generalizes and provides a unified treatment of the Gevrey regularity result of Foias and Temam in the space periodic case and those of Le Jan and Sznitman and Lemarié–Rieusset in the whole space with no boundary.