Gevrey regularity with weight for incompressible Euler equation in the half plane

TL;DR

This paper establishes weighted Gevrey regularity for solutions to the incompressible Euler equation in the half-plane, addressing decay at infinity and the pressure estimate challenges, with implications for boundary layer problems.

Contribution

It introduces a method to prove weighted Gevrey regularity for Euler solutions with polynomial decay, advancing understanding of boundary layer equations in rotating fluids.

Findings

Weighted Gevrey regularity is proven for Euler solutions.

The method handles pressure estimates with weight functions.

Results are relevant for boundary layer analysis in fluid dynamics.

Abstract

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted $L^2$- estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.