Logarithmically regularized inviscid models in borderline sobolev spaces
- Authors
- Chae, Dongho; Wu, Jiahong
- Issue Date
- Nov-2012
- Publisher
- AMER INST PHYSICS
- Keywords
- partial differential equations
- Citation
- JOURNAL OF MATHEMATICAL PHYSICS, v.53, no.11
- Journal Title
- JOURNAL OF MATHEMATICAL PHYSICS
- Volume
- 53
- Number
- 11
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/20079
- DOI
- 10.1063/1.4725531
- ISSN
- 0022-2488
1089-7658
- Abstract
- Several inviscid models in hydrodynamics and geophysics such as the incompressible Euler vorticity equations, the surface quasi-geostrophic equation, and the Boussinesq equations are not known to have even local well-posedness in the corresponding borderline Sobolev spaces. Here H-s is referred to as a borderline Sobolev space if the L-infinity-norm of the gradient of the velocity is not bounded by the H-s-norm of the solution but by the H-(s) over tilde-norm for any (s) over tilde > s. This paper establishes the local well-posedness of the logarithmically regularized counterparts of these inviscid models in the borderline Sobolev spaces. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4725531]
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