Boundedness for large \(| x|\) of suitable weak solutions of the Navier-Stokes equations with prescribed velocity at infinity
The author investigates the boundedness of weak solutions to the Navier- Stokes equations in exterior domains; the result refers to solutions which are perturbations of PR-solutions, a class of stationary flows introduced by R. Finn, which describe the fluid past a body that moves with constant velocity \(v_ \infty\neq 0\). Known results refer to the case \(v_ \infty=0\) or require the PR-solution to be small. The core of the proof consists of an extension of a criterion originally due to Caffarelli, Kohn and Nirenberg, which allows to infer boundedness from a growth property of an integral norm over parabolic cylinders.
Navier-Stokes equations in exterior domains
scientific article; zbMATH DE number 169099
scientific article