Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4611925 | Journal of Differential Equations | 2011 | 33 Pages |
Abstract
In this article we consider the following generalized quasi-geostrophic equation∂tθ+u⋅∇θ+νΛβθ=0,u=ΛαR⊥θ,x∈R2, where ν>0ν>0, Λ:=−Δ, α∈]0,1[α∈]0,1[ and β∈]0,2[β∈]0,2[. We first show a general conditional criterion yielding the nonlocal maximum principles for the whole space active scalars, then mainly by applying the general criterion, for the case α∈]0,1[α∈]0,1[ and β∈]α+1,2]β∈]α+1,2] we obtain the global well-posedness of the system with smooth initial data; and for the case α∈]0,1[α∈]0,1[ and β∈]2α,α+1]β∈]2α,α+1] we prove the local smoothness and the eventual regularity of the weak solution of the system with appropriate initial data.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Changxing Miao, Liutang Xue,