Abstract
We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by introducing a smoothing operator of nonzero but possibly arbitrarily small degree. This family naturally interpolates between the 2D Euler equation and the SQG equation. For this family of equations we construct an invariant measure on a rough $$L^2$$ -based Sobolev space and establish the existence of solutions of arbitrarily large lifespan for initial data in a set of full measure in the rough Sobolev space.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Stochastics and Partial Differential Equations: Analysis and Computations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.