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Spatial-decay of solutions to the quasi-geostrophic equation with the critical and the super-critical dissipation
- Publication Year :
- 2018
-
Abstract
- The initial value problem for the two-dimensional dissipative quasi-geostrophic equation derived from geophysical fluid dynamics is studied. The dissipation of this equation is given by the fractional Laplacian. It is known that the half Laplacian is a critical dissipation for the quasi-geostrophic equation. The global existence of solutions upon the suitable condition is also well known, and that solutions of a fractional dissipative equation decay with a polynomial order as the spatial variable tends to infinity. In this paper, far field asymptotics of solutions to the quasi-geostrophic equation are given in the critical and the supercritical cases. Those estimates are derived from the energy methods for the difference between the solution and its asymptotic profile.
- Subjects :
- Anomalous diffusion
Applied Mathematics
010102 general mathematics
Mathematical analysis
Mathematics::Analysis of PDEs
General Physics and Astronomy
Statistical and Nonlinear Physics
Fluid mechanics
Dissipation
01 natural sciences
010101 applied mathematics
Mathematics - Analysis of PDEs
Geophysical fluid dynamics
Dissipative system
FOS: Mathematics
Initial value problem
0101 mathematics
Laplace operator
Mathematical Physics
Geostrophic wind
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....fd9adfc5dcf4ea4ac7439fcd24adcd04