XLI. On steady motion in an incompressible viscous fluid

Motion of an Elastic Solid inside an Incompressible Viscous Fluid

The motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature. Mathematically, such motion is described by a PDE system that couples the parabolic and hyperbolic phases, the latter inducing a loss of regularity which has left the basic question of existence open until now. In this paper, we prove the existence and uniqueness of such motions (locally in time), whe...

Mathematical models of turbulent motion of an incompressible viscous fluid

Pattern Selection for Faraday Waves in an Incompressible Viscous Fluid

Abstract. When a layer of fluid is oscillated up and down with a sufficiently large amplitude patterns form on the surface: a phenomenon first observed by Faraday. A wide variety of such patterns have been observed from regular squares and hexagons to superlattice and quasipatterns and more exotic patterns such as oscillons. Previous work has investigated the mechanisms of pattern selection usi...

On Local Existence of Solutions of the Free Boundary Problem for an Incompressible Viscous Self-gravitating Fluid Motion

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that u ∈W 2,1 r (Ω̃ T ) with r > 3. The existence is proved by the method of successive approximations where the solvability of the Cauchy– Neumann problem for the Stok...

Nested Cartesian grid method in incompressible viscous fluid flow

Article history: Received 15 January 2009 Received in revised form 16 April 2010 Accepted 28 May 2010 Available online 8 June 2010