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

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Original research article

Author(s):

Hernán Cabrales^a, Tovias Castro^b, John Moreno^c, Osmir Olivera^d

^a Universidad de la Costa, Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia.
^b Departamento de Matemáticas, Universidad del Atlántico, Barranquilla, Colombia.
^c Facultad de Ingeniería, Corporación Universitaria Remington, Medellín, Colombia.
^d Departamento de Matemáticas, Universidad del Atlántico, Barranquilla, Colombia.

Advances in the Theory of Nonlinear Analysis and its Applications 7(3), 45–66.

Received: March 15, 2023

Accepted: October 19, 2023

Published: October 21, 2023

Abstract

In this paper, we show some mathematical properties for a nonlinear system of partial differential equations that describe the dynamics of internal motions of an exponentially stratified fluid in three-dimensional space. Basically, we study the existence and uniqueness of the weak solution for our system of partial differential equations involving the nonlinear advection term on a finite interval.

Keywords: Stratified fluids; Non-viscous fluids; Nonlinear advection term; System of partial differential equations; Sobolev spaces; Galerkin method.

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APA Style

Cabrales, H., Castro, T., Moreno, J., & Olivera, O. (2023). Study of a nonlinear system of partial differential equations associated with stratified fluids in three dimensions. Advances in the Theory of Nonlinear Analysis and Its Application, 7(3), 45–66.