On the Existence and Uniqueness of Solutions for Nonlinear System Modeling Three-Dimensional Viscous Stratified Flows

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.

Study of a Nonlinear System of Partial Differential Equations Associated with Stratified Fluids in Three Dimensions

“…They got solutions with some nicely regular properties; see, for example, the theorem given on page 12 of [23]. Moreover, one of the authors treated a more regular part of this system, for example, in [12], having success obtaining solutions with some friendly classical properties due to the presence of a dissipative term. Therefore, the properties described in this article are novel and valuable since we do not have the system's regulator.…”