Regularization by Noise of an Averaged Version of the Navier–Stokes Equations
Theresa Lange
Abstract
In Tao 2016, the author constructs an averaged version of the deterministic three-dimensional Navier-Stokes equations (3D NSE) which experiences blow-up in finite time. In the last decades, various works have studied suitable perturbations of ill-behaved deterministic PDEs in order to prevent or delay such behavior. A promising example is given by a particular choice of stochastic transport noise closely studied in Flandoli et al. 2021. We analyze the model in Tao 2016 in view of these results and discuss the regularization skills of this noise in the context of the averaged 3D NSE.
Topics & Concepts
Regularization (linguistics)MathematicsOrdinary differential equationPartial differential equationApplied mathematicsNavier–Stokes equationsContext (archaeology)Noise (video)Mathematical analysisDifferential equationComputer sciencePhysicsMechanicsArtificial intelligenceCompressibilityImage (mathematics)BiologyPaleontologyNavier-Stokes equation solutionsFluid Dynamics and Turbulent FlowsStochastic processes and financial applications