Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations
| Autor: | Susan Friedlander, Anthony Suen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Drift velocity Advection Mechanical Engineering 010102 general mathematics Constitutive equation Mathematical analysis Scalar (physics) Context (language use) 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs Mathematics (miscellaneous) Geophysical fluid dynamics Attractor FOS: Mathematics 0101 mathematics Diffusion (business) 76D03 35Q35 76W05 Analysis Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2005.10667 |
| Popis: | We investigate the properties of an abstract family of advection diffusion equations in the context of the fractional Laplacian. Two independent diffusion parameters enter the system, one via the constitutive law for the drift velocity and one as the prefactor of the fractional Laplacian. We obtain existence and convergence results in certain parameter regimes and limits. We study the long time behaviour of solutions to the general problem and prove the existence of a unique global attractor. We apply the results to two particular active scalar equations arising in geophysical fluid dynamics, namely the surface quasigeostrophic equation and the magnetogeostrophic equation. |
| Databáze: | OpenAIRE |
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