Strong ill-posedness for SQG in critical Sobolev spaces
In-Jee Jeong, Junha Kim
Abstract
We prove that the inviscid surface quasigeostrophic (SQG) equations are strongly ill-posed in critical Sobolev spaces: there exists an initial data H 2 ޔ( 2 ) without any solutions in L ∞ t H 2 .Moreover, we prove strong critical norm inflation for C ∞ -smooth data.Our proof is robust and extends to give similar ill-posedness results for the family of modified SQG equations which interpolate the SQG with the two-dimensional incompressible Euler equations.
Topics & Concepts
Sobolev spaceMathematicsWell-posed problemPure mathematicsMathematical analysisAdvanced Mathematical Physics ProblemsNavier-Stokes equation solutionsStability and Controllability of Differential Equations