On the existence of solutions to the planar exterior Navier Stokes system
Matthieu Hillairet (CEREMADE), Peter Wittwer

TL;DR
This paper proves the existence of solutions to the stationary incompressible Navier-Stokes equations in the exterior of a disk with specific boundary conditions, expanding understanding of fluid flow around obstacles.
Contribution
It establishes the existence of solutions for a broad set of boundary conditions without symmetry assumptions, filling a gap in the mathematical theory of exterior flows.
Findings
Existence of solutions proven for non-zero boundary conditions
Solutions exist without symmetry assumptions
Applicable to exterior flow problems around disks
Abstract
We consider the stationary incompressible Navier Stokes equation in the exterior of a disk B with non-zero Dirichlet boundary conditions on the disk and zero boundary conditions at infinity. We prove the existence of solutions for an open set of boundary conditions without symmetry.
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Taxonomy
TopicsNavier-Stokes equation solutions · Differential Equations and Boundary Problems · Advanced Mathematical Modeling in Engineering
