Dissipative Quasigeostrophic Dynamics under Random Forcing

1998/05/25 by James R. Brannan, Brannan, James R., Jinqiao Duan +3
Mathematics · #35Q35 #58F39 #76U05 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35Q35 #msc:58F39 #msc:76U05

paper · pdf · doi:10.48550/arxiv.math/9805113

LaTeX, 15 pages

arxiv created 1998/05/25 · arxiv updated 2009/11/30

Abstract

The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasigeostrophic equation whose well-posedness is well-known, there seems no rigorous result on global existence and uniqueness of the randomly forced quasigeostrophic equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions.

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