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...

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...

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the phys...

We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and distance, and of vanishing viscosity. Under suitable conditions on the particle size, particle distance, and viscosity, we prove that solutions of the Navier-Stok...

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

Entropy generation due to viscous incompressible MHD forced convective dissipative fluid flow through a horizontal channel of finite depth in the existence of an inclined magnetic field and heat source effect has been examined. The governing non-linear partial differential equations for momentum, energy and entropy generation are derived and solved by using the analytical method. In addition; t...

In this study we consider the problem of the interface motion under the capillary–gravity and an external electric force. The infinitely deep fluid layer is assumed to be viscous, perfectly conducting and the flow to be incompressible. The weak viscous effects are introduced using the Helmholtz–Leray decomposition and the visco-potential flow approach. The electric charge distributions above an...