Photo from academic.microsoft.com
We give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of… Click to show full abstract
We give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of the n-dimensional Euler equations in the class $$C^1\cap L^2 (\Omega )$$ and also in $$C^k \cap L^2(\Omega )$$ where $$\Omega $$ can be the whole space, a smooth bounded domain, or the torus. We also apply our method to the Oldroyd B, surface quasi-geostrophic, and Boussinesq systems.
Keywords:
arising hydrodynamics;
class;
class equations;
equations arising;
hydrodynamics;
ill posedness
Journal Title: Archive for Rational Mechanics and Analysis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Archive for Rational Mechanics and Analysis
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!