Spatial asymptotic expansions in the incompressible Euler equation

Abstract

In this paper we prove that the Euler equation describing the motion of an ideal fluid in ${\mathbb{R}}^d$ is well-posed in a class of functions allowing spatial asymptotic expansions as $|x|\to \infty$ of any a priori given order. These asymptotic expansions can involve log terms and lead to a family of conservation laws. Typically, the solutions of the Euler equation with initial data in the Schwartz class develop non-trivial spatial asymptotic expansions of the type considered here.

References in corpus (2)

• An integrable shallow water equation with peaked solitons
• Asymptotics of spectral quantities of Zakharov-Shabat operators