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A Posteriori Error Estimates for Self-Similar Solutions to the Euler Equations

By Alberto Bressan and Wen Shen

Abstract

The main goal of this paper is to analyze a family of "simplest possible" initial data for which, as shown by numerical simulations, the incompressible Euler equations have multiple solutions. We take here a first step toward a rigorous validation of these numerical results. Namely, we consider the system of equations corresponding to a self-similar solution, restricted to a bounded domain with smooth boundary. Given an approximate solution obtained via a finite dimensional Galerkin method, we establish a posteriori error bounds on the distance between the numerical approximation and the exact solution having the same boundary data

Topics: Mathematics - Analysis of PDEs, 35L60, 35Q31, 35Q35
Year: 2020
OAI identifier: oai:arXiv.org:2002.01962

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