Non existence and strong ill-posedness in C and Sobolev spaces for SQG
Diego Córdoba, Luis Martínez-Zoroa
Abstract
We construct solutions in R2 with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in Ck (k≥2) but that are not in Ck for t>0. We prove a similar result also for Hs in the range s∈(32,2). Moreover, we prove strong ill-posedness in the critical space H2.
Topics & Concepts
MathematicsSobolev spaceSpace (punctuation)Range (aeronautics)Surface (topology)Energy (signal processing)Construct (python library)Pure mathematicsMathematical analysisGeometryStatisticsPhilosophyProgramming languageMaterials scienceComposite materialLinguisticsComputer scienceNavier-Stokes equation solutionsGeometric Analysis and Curvature FlowsAdvanced Mathematical Physics Problems