Strong solutions to the Navier-Stokes equations on thin 3D domains
By B. Nowakowski, W. Zajkaczkowski. 2012
51 citations recorded by the source corpus.
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 Poincar\'e 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.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3c12ed0c4f28ebdb0d1a05aaa652796b3db789f6
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- The uniform Korn–Poincaré inequality in thin domains (2008, background): “The study of the global existence and asymptotic properties of solutions to the Navier–Stokes equations in thin 3d domains began with Raugel and Sell in [21].”