We consider the problem of evolution of a finite isolated mass of a viscous incompressible liquid with a free surface. We assume that the initial configuration of the liquid hasn arbitrary shape, the initial free boundary possesses a certain regularity and the initial velocity satisfies only natural compatibility and regularity conditions (but its smallness is not assumed). We prove that this problem is well posed, i. e., we construct a local in time solution belonging to some Sobolev-Slobodetskii spaces. We expect that this result can be helpful for the analysis of more complicated problems, for instance, problems of magnetohydrodynamics. Bibliography: 9 titles. © 2010 Springer Science+Business Media, Inc.
On the local solvability of free boundary problem for the Navier-Stokes equations
PADULA, Mariarosaria;
2010
Abstract
We consider the problem of evolution of a finite isolated mass of a viscous incompressible liquid with a free surface. We assume that the initial configuration of the liquid hasn arbitrary shape, the initial free boundary possesses a certain regularity and the initial velocity satisfies only natural compatibility and regularity conditions (but its smallness is not assumed). We prove that this problem is well posed, i. e., we construct a local in time solution belonging to some Sobolev-Slobodetskii spaces. We expect that this result can be helpful for the analysis of more complicated problems, for instance, problems of magnetohydrodynamics. Bibliography: 9 titles. © 2010 Springer Science+Business Media, Inc.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
