an:01045411
Zbl 0880.76090
Desjardins, Beno??t
Regularity results for two-dimensional flows of multiphase viscous fluids
EN
Arch. Ration. Mech. Anal. 137, No. 2, 135-158 (1997).
00040794
1997
j
76T99 76N10 35Q35 35B65
weak solutions; Navier-Stokes equations; integral curves; strong solutions
Summary: Global regularity results for weak solutions of the Navier-Stokes equations for two-dimensional multiphase incompressible fluids are proved under suitable conditions on the viscosity without assuming positive lower bounds on the initial density. As an application, we deduce regularity properties for the integral curves of the corresponding velocity field. Finally, we prove regularity results ``in the small'' for strong solutions.