TITLE:
On the Existence and Uniqueness of Solutions for Nonlinear System Modeling Three-Dimensional Viscous Stratified Flows
AUTHORS:
Andrei Giniatoulline, Tovias Castro
KEYWORDS:
Partial Differential Equations, Sobolev Spaces, Fluid Dynamics, Stratified Fluid, Viscous Fluid
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.7,
June
13,
2014
ABSTRACT: We establish the uniqueness and local existence of weak solutions for a
system of partial differential equations which describes non-linear motions of
viscous stratified fluid in a homogeneous gravity field. Due to the presence of
the stratification equation for the density, the model and the problem are new
and thus different from the classical Navier-Stokes equations.