Global existence of the three‐dimensional compressible Euler equations for generalized Chaplygin gas with damping

Abstract

In this paper, we establish a global existence (GE) result for the threedimensional compressible Euler equations (CEE) for generalized Chaplygin gas (GCG) with damping. More precisely, by transforming the three-dimensional CEE for GCG with damping to a symmetric hyperbolic system, one shows that the total energy in H 3 is strictly decaying with time for any sufficiently small initial data. As a result, the GE result follows from the local well-posedness of the system in H 3. This gives the first GE result relating to the three-dimensional CEE.