Well-posedness for a stochastic 2D Euler equation with transport noise
Oana Lang, Dan Crisan
2022Stochastic Partial Differential Equations Analysis and Computations24 citationsDOIOpen Access PDF
Abstract
We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.
Topics & Concepts
Euler equationsSmoothnessEuler's formulaNoise (video)CompressibilityMathematical analysisVorticityMathematicsSemi-implicit Euler methodEuler methodBackward Euler methodPhysicsVortexComputer scienceMechanicsImage (mathematics)Artificial intelligenceNavier-Stokes equation solutionsStochastic processes and financial applicationsFluid Dynamics and Turbulent Flows