Journal article
GLOBAL WELLPOSEDNESS AND BLOWUP OF SOLUTIONS TO A NONLOCAL EVOLUTION PROBLEM WITH SINGULAR KERNELS
Communications on pure and applied analysis, Vol.9(6), pp.1591-1606
11/01/2010
DOI: 10.3934/cpaa.2010.9.1591
Abstract
We consider a nonlocal evolution equation in R(2): partial derivative(u)(t) + del. (uK * u) = 0, where K(x) = mu x/vertical bar x vertical bar alpha, mu = +/- 1 and 1 < alpha < 2. We study wellposedness, continuation/blowup criteria and smoothness of solutions in Sobolev spaces. In the repulsive case (mu = 1), by using the sharp blowup criteria, we prove global wellposedness for any positive large initial data. In the attractive case (mu = -1), by using a novel free energy inequality together with a mass localization technique, we construct finite time blowups for a large class of smooth initial data.
Details
- Title: Subtitle
- GLOBAL WELLPOSEDNESS AND BLOWUP OF SOLUTIONS TO A NONLOCAL EVOLUTION PROBLEM WITH SINGULAR KERNELS
- Creators
- Dong Li - Univ Iowa, Dept Math, Iowa City, IA 52242 USAXiaoyi Zhang - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Communications on pure and applied analysis, Vol.9(6), pp.1591-1606
- Publisher
- AMER INST MATHEMATICAL SCIENCES
- DOI
- 10.3934/cpaa.2010.9.1591
- ISSN
- 1534-0392
- eISSN
- 1553-5258
- Number of pages
- 16
- Grant note
- Mathematics Department of University of Iowa University of Iowa DMS-0635607 / National Science Foundation 0908032 / NSF Alfred P. Sloan Research Fellowship
- Language
- English
- Date published
- 11/01/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9984241158602771
Metrics
39 Record Views