Geodesic
Quasi-geostrophic type equations with weak initial data
Electronic Journal of Differential Equations, Tome 1998 (1998).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a10/}
}
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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/