Mixed Initial-Boundary Value Problem for the Three-Dimensional Navier-Stokes Equations in Polyhedral Domains

2011/02/13 by Michal Beneš, Michal Benes, Benes, Michal
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1102.2584

10 pages

arxiv created 2011/02/13 · openalex publication_date 2011/02/13 · arxiv updated 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a mixed initial-boundary value problem for the Navier-Stokes equations, where the Dirichlet, Neumann and slip boundary conditions are prescribed on the faces of a three-dimensional polyhedral domain. We prove the existence, uniqueness and smoothness of the solution on a time interval (0,T^*), where 0<T^*≤ T.

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