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arXiv · 2306.00319

On stationary Navier-Stokes equations in the upper-half plane

Adrian D. Calderon·Van Le·Tuoc Phan
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Abstract

We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on the external forces. Weak-strong uniqueness criteria based on various growth conditions at the infinity of weak solutions are also given. This is done by employing an energy estimate and a Hardy's inequality. Several estimates of stream functions are carried out and two density lemmas with suitable weights for the homogeneous Sobolev space on 2 dimensional space are proved.

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Adrian D. Calderon, Van Le, Tuoc Phan. 2023-06-01. On stationary Navier-Stokes equations in the upper-half plane. https://arxiv.org/abs/2306.00319

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