Geodesic
Quasi-geostrophic type equations with weak initial data
Electronic journal of differential equations, Tome 1998 (1998)
We study the initial value problem for the quasi-geostrophic type equations

$ \displaylines{ {\partial \theta \over \partial t}+u\cdot\nabla\theta + (-\Delta)^{\lambda}\theta=0,\quad \hbox{on } {\Bbb R}^n\times (0,\infty), \cr \theta(x,0)=\theta_0(x), \quad x\in {\Bbb R}^n\,, \cr} $

where

$ {1 \over2}\lambda \le 1,\quad 1 less than p less than \infty, \quad {n\over p}\le 2\lambda -1, \quad r={n\over p}-(2\lambda-1) \le 0\,. $

We also prove that the solution is global if $\theta_0$ is sufficiently small.
Classification : 35K22, 35Q35, 76U05
Keywords: quasi-geostrophic equations, weak data, well-posedness 
@article{EJDE_1998__1998__a10,
     author = {Wu,  Jiahong},
     title = {Quasi-geostrophic type equations with weak initial data},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {0898.35077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a10/}
}
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VL  - 1998
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%0 Journal Article
%A Wu,  Jiahong
%T Quasi-geostrophic type equations with weak initial data
%J Electronic journal of differential equations
%D 1998
%V 1998
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a10/
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%F EJDE_1998__1998__a10
Wu,  Jiahong. Quasi-geostrophic type equations with weak initial data. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a10/