Affiliations: Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic | Department of Mathematics Education, Mokpo National University, Muan, South Korea | IMATH, EA2134, Université de Toulon, La Garde, France
Note: [] Corresponding author: Eduard Feireisl, Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic. E-mail: [email protected]
Abstract: We consider the motion of a compressible viscous fluid in the asymptotic regime of low Mach and high Reynolds numbers under strong stratification imposed by a conservative external force. Assuming a bi-dimensional character of the flow, we identify the limit system represented by the so-called lake equation – the Euler system supplemented by an anelastic type constraint imposed by the limit density profile. The key ingredient of the proof are new “frequency localized” estimates of Strichartz type.
