Global existence of smooth solutions to 2D Chaplygin gases on curved space (Q2830332)

The authors consider two-dimensional isentropic flow of Chaplygin gas on some asymptotically flat Riemann manifold. Metric tensor is diagonal with equal time-dependent quantity \(a\) on the diagonal, and it tends to 1 as \(t\to\infty\). The state equation \(P=P_0-A/\rho\) connects pressure with density. Initial density distribution is constant plus small perturbation with compact support; initial velocity field is just a small compactly supported perturbation of zero. The main result is existence of a unique global solution provided that perturbations are small enough, initial velocity field is irrotational (i.e. potential) and metric tensor components decay quickly enough. The proof is done by the method of continuity.