Maximal regularity and viscous incompressible flows with free interface
Volume 81 / 2008
Banach Center Publications 81 (2008), 471-480
MSC: Primary 35Q30; Secondary 76D07.
DOI: 10.4064/bc81-0-29
Abstract
We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time $L_p$-$L_q$ maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.
