The initial value problem for the Navier-Stokes equations in Lm(Rm)

• Autor: Machaca, Magdalena Huacasi
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/16123
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/16123
• Nivel de acceso: acceso abierto
• Materia: Navier-Stokes Equations; Leray Projector; Lebesgue Spaces; Null divergence spaces; Existence and Uniqueness; Ecuaciones de Navier-Stokes; Proyector de Leray; Espacios de Lebesgue;Espacios de divergencia nula; Existencia y Unicidad

In this paper addresses the initial value problem for the Navier-Stokes equations in Rm (m = 2; 3;..) with initial condition in the subspace PLp(Rm) of Lp(Rm), characterized by the null divergence condition. The problem is studied considering its integral formulation, where an argument of successive approximations is used. The existence and uniqueness of the local solution is proven depending on a condition of smallness in the time of existence. On the other hand, the overall result is tested with a small amount of the initial data.