Proceedings of the American Mathematical Society · 2019 · 13 citations · 11 references
Natural SciencesPhysicsFluid DynamicsFluid MechanicsNavier-stokes EquationsVortex DynamicsElliptic FunctionsLipschitz ConditionsLipschitz ContinuityStream FunctionVortex Flow
In this note, we give a general criterion for steady vortex flows in a planar bounded domain. More specifically, we show that if the stream function satisfies “locally” a semilinear elliptic equation with monotone or Lipschitz nonlinearity, then the flow must be steady.
11
Topological Methods in Hydrodynamics
Vladimir I. Arnold, Boris Khesin · Annual Review of Fluid Mechanics · 1992 · 1.1K citations
Computing, Physics, Fluid Dynamics +14