Spatial asymptotic expansions in the incompressible Euler equation

2016/06/26 by Robert McOwen, McOwen, R., Peter Topalov +1
Mathematics · Physics and Astronomy · #35B40 #35Q31 #35Q35 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1606.08059

openalex publication_date 2016/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove that the Euler equation describing the motion of an ideal fluid in \R^d is well-posed in a class of functions allowing spatial asymptotic expansions as |x|→∞ 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.

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