Motion of slightly compressible fluids in a bounded domain. II

Abstract

We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of non-linear equations.

to appear in Communications in Contemporary Mathematics

References in corpus (2)

• The free boundary Euler equations with large surface tension
• On the limit of large surface tension for a fluid motion with free boundary

Cited by in corpus (5)

• Rough sound waves in $3D$ compressible Euler flow with vorticity
• The free boundary Euler equations with large surface tension
• Local Well-posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics
• The relativistic Euler equations: Remarkable null structures and regularity properties
• On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid