In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the free boundary isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions expands at a linear rate in time. We show that if the adiabatic exponent gamma belongs to the interval (1, 5/3] then these affine motions are nonlinearly stable; small perturbations lead to global-in-time solutions that remain "close" to the moduli space of affine solutions and no shocks are formed in the process. Our strategy relies on two key ingredients: a new interpretation of the affine motions using an (almost) invariant action of GL(3) on the compressible Euler system and the use of Lagrangian coordinates. The former suggests a particular rescaling of time and a change of variables that elucidates a stabilisation mechanism, while the latter requires new ideas with respect to the existing well-posedness theory for vacuum free boundary fluid equations. This is joint work with Juhi Jang (USC).

# Expanding large global solutions of the equations of compressible fluid mechanics

Speaker:

Mahir Hadzic (KCL)

Date/Time:

Wed, 08/03/2017 - 15:00

Room:

Queens Building W316

Seminar series: