On the Solutions in the Large of the Two-Dimensional Flow of a Non-Viscous Incompressible Fluid.

摘要

We study the Euler equations (1.1) for the motion of a non-viscous incompressible fluid in a plane domain omega. Let E be the Banach space defined in (1.4), let the initial data (V sub 0) belong to E, and let the external forces f(t) belong to L(sub Loc) (R;E). In theorem 1.1 we prove the continuity and the global boundedness of the (unique) solution v(t), and in theorem 1.2 we prove the strong-continuous dependence of v on the data (V sub 0) and f. In particular, the vorticity rot v(t) is a continuous function in omega, for every t epsilon if and only if this property holds for one value of t. In theorem 1/3 we state some properties for the associated group of nonlinear operators S(t). Finally, in theorem 1.4 we give a quite general sufficient condition on the data in order to get classical solutions.