quasi-geostrophic type equations with weak initial data
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ID: 227300
1998
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Abstract
We study the initial value problem for the quasi-geostrophic type equations $$ displaylines{ {partial heta over partial t}+ucdotablaheta + (-Delta)^{lambda}heta=0,quad hbox{on } {Bbb R}^nimes (0,infty), cr heta(x,0)=heta_0(x), quad xin {Bbb R}^n,, cr} $$ where $lambda$, ($0leq lambda leq 1$) is a fixed parameter and $u=(u_j)$ is divergence free and determined from $heta$ through the Riesz transform $u_j=pm {cal R}_{pi(j)}heta$, with $pi(j)$ a permutation of $1,2,cdots,n$. The initial data $heta_0$ is taken in the Sobolev space $dot{L}_{r,p}$ with negative indices. We prove local well-posedness when $$ {1 over2}
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| Reference Key |
wu1998electronicquasi-geostrophic
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| Authors | ;Jiahong Wu |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 1998 |
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