Existence and decay of solutions of the 2D QG equation in the presence of an obstacle

Leonardo Kosloff; Tomas Schonbek

doi:10.3934/dcdss.2014.7.1025

Article Contents

2014, Volume 7, Issue 5: 1025-1043. Doi: 10.3934/dcdss.2014.7.1025

This issue Previous Article Convergent finite differences for 1D viscous isentropic flow in Eulerian coordinates Next Article Stokes and Navier-Stokes equations with perfect slip on wedge type domains

Existence and decay of solutions of the 2D QG equation in the presence of an obstacle

Leonardo Kosloff^1, and
Tomas Schonbek^2,

1.
Department of Mathematics, UC Riverside, 900 University Ave, Riverside, CA 92521
2.
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431

Received: February 28, 2013

Published: September 2014

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Abstract

We continue the study initiated in [16] of dissipative differential equations governing fluid motion in the presence of an obstacle, in which the dissipative term is given by the Laplacian, or a fractional power of the Laplacian. Our main tools are the Ikebe-Ramm transform, and the localized version of the fractional Laplacian due to Caffarelli and Silvestre [5] as improved by Stinga and Torrea [21]. We give applications to the problem of existence of weak solutions of the two dimensional dissipative quasi-geostrophic equation and the decay of these solutions in the $L^2$-norm.

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Mathematics Subject Classification: Primary: 35J05, 35P05, 35Q30, 35Q35.

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References

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