Wellposedness and regularity of solutions of an aggregation equation
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 261-294 / Harvested from Project Euclid
We consider an aggregation equation in $\mathbb R^d$, $d\ge 2$ with fractional dissipation: $u_t + \nabla\cdot(u \nabla K*u)=-\nu \Lambda^\gamma u $, where $\nu\ge 0$, $0 < \gamma\le 2$ and $K(x)=e^{-|x|}$. In the supercritical case, $0 < \gamma < 1$, we obtain new local wellposedness results and smoothing properties of solutions. In the critical case, $\gamma=1$, we prove the global wellposedness for initial data having a small $L_x^1$ norm. In the subcritical case, $\gamma > 1$, we prove global wellposedness and smoothing of solutions with general $L_x^1$ initial data.
Publié le : 2010-03-15
Classification:  Aggregation equations,  well-posedness,  higher regularity,  35A05,  35A07,  35B45,  35R10
@article{1266330124,
     author = {Li
, 
Dong and Rodrigo
, 
Jos\'e L.},
     title = {Wellposedness and regularity of solutions of an aggregation equation},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 261-294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1266330124}
}
Li
, 
Dong; Rodrigo
, 
José L. Wellposedness and regularity of solutions of an aggregation equation. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  261-294. http://gdmltest.u-ga.fr/item/1266330124/