We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-6,
author = {Shouquan Ma and Guixiang Xu},
title = {Global well-posedness and blow up for the nonlinear fractional beam equations},
journal = {Applicationes Mathematicae},
volume = {37},
year = {2010},
pages = {353-373},
zbl = {1206.35246},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-6}
}
Shouquan Ma; Guixiang Xu. Global well-posedness and blow up for the nonlinear fractional beam equations. Applicationes Mathematicae, Tome 37 (2010) pp. 353-373. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am37-3-6/