Strong solutions to the Navier-Stokes equations on thin 3D domains

2012/04/26 by Bernard Nowakowski, B. Nowakowski, Wojciech M. Zajączkowski +3
Engineering · Mathematics · #35Q30 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35Q30 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1204.5988

arxiv created 2012/04/26 · openalex publication_date 2012/04/26 · arxiv updated 2012/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of strong solutions to Navier-Stokes equations in three dimensional thin domains. Our proof is based on the energy and the Poincaré inequalities as well as contraction principle argument and is free of the mean value operator. The price we pay for the simplicity of the proof are stronger assumptions on the initial velocity and the forcing term. We need to assume that their derivatives with respect to time belong to certain Lebesgue space.

Related

• Some results on the Navier-Stokes equations in thin 3D domains
• Large-time behavior of the weak solution to 3D Navier-Stokes equations
• Existence of Strong Solutions for the 3D Navier-Stokes System
• 3D Navier-Stokes Equations with Nonvanishing Boundary Condition
• Topological Properties of Strong Solutions for the 3D Navier-Stokes Equations