Affiliation:
1. Department of Mathematics Princeton University Princeton New Jersey USA
2. Department of Mathematics Temple University Philadelphia Pennsylvania USA
3. Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China
Abstract
AbstractWe prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in . We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof then uses the method of the nonlinear maximum principle for nonlocal operators in the extended system.
Funder
National Science Foundation
Chinese Academy of Sciences
National Natural Science Foundation of China
National Key Research and Development Program of China
Reference22 articles.
1. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
2. Positive solutions of nonlinear problems involving the square root of the Laplacian
3. K.Chen R.Hu andQ.‐H.Nguyen Well‐posedness for local and nonlocal quasilinear evolution equations in fluids and geometry arXiv:2407.05313 math.AP.
4. Geometric Statistics in Turbulence
5. Remarks on the fractional Laplacian with Dirichlet boundary conditions and applications;Constantin P.;IMRN,2017
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献