A direct approach to nonuniqueness and failure of compactness for the SQG equation
Philip Isett, Andrew Ma
Abstract
Abstract We give an alternative proof of the nonuniqueness of weak solutions to the surface quasigeostrophic equation (SQG) first shown in [3]. Our approach proceeds directly at the level of the scalar field. Furthermore, we prove that every smooth scalar field with compact support that conserves the integral can be realized as a weak limit of solutions to SQG.
Topics & Concepts
MathematicsCompact spaceLimit (mathematics)Mathematical analysisScalar (mathematics)Scalar fieldSurface (topology)Weak solutionField (mathematics)Applied mathematicsVector fieldIntegral equationConstant (computer programming)Navier-Stokes equation solutionsGeometric Analysis and Curvature FlowsNonlinear Partial Differential Equations