On a singular limit for the stratified compressible Euler system

Article type: Research Article

Authors: Feireisl, Eduard^{a; b; *} | Tang, Tong^{a; c}

Affiliations: [a] Institute of Mathematics of the Academy of Sciences of the Czech Republic, Zitna 25, 11567, Praha 1, Czech Republic. E-mail: feireisl@math.cas.cz | [b] Technical University Berlin, Institute of Mathematics, Strasse des 17. Juni 136, 10623 Berlin, Germany | [c] Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, P.R. China. E-mail: tt0507010156@126.com

Correspondence: [*] Corresponding author. E-mail: feireisl@math.cas.cz.

Abstract: We consider a singular limit for the compressible Euler system in the low Mach number regime driven by a large external force. We show that any dissipative measure-valued solution approaches a solution of the lake equation in the asymptotic regime of low Mach and Froude numbers. The result holds for the ill-prepared initial data creating rapidly oscillating acoustic waves. We use dispersive estimates of Strichartz type to eliminate the effect of the acoustic waves in the asymptotic limit.

Keywords: Compressible Euler equations, singular limit, low Mach number, low Froude number, dissipative measure-valued solutions

DOI: 10.3233/ASY-191518

Journal: Asymptotic Analysis, vol. 114, no. 1-2, pp. 59-72, 2019