Geodesic
Global well-posedness and blow up for the nonlinear fractional beam equations
Shouquan Ma 1   ; Guixiang Xu 2
1 Graduate School China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088
2 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088
Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 353-373 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/am37-3-6
Keywords: establish strichartz estimates linear fractional beam equations besov spaces using these estimates obtain global well posedness subcritical critical defocusing fractional beam equations course assume small initial critical addition convexity method blow occurs focusing fractional beam equations negative energy

Shouquan Ma  1   ; Guixiang Xu  2

1 Graduate School China Academy of Engineering Physics P.O. Box 2101 Beijing, China, 100088
2 Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing, China, 100088 
@article{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},
     pages = {353--373},
     year = {2010},
     volume = {37},
     number = {3},
     doi = {10.4064/am37-3-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am37-3-6/}
}
TY  - JOUR
AU  - Shouquan Ma
AU  - Guixiang Xu
TI  - Global well-posedness and blow up for
 the nonlinear fractional beam equations
JO  - Applicationes Mathematicae
PY  - 2010
SP  - 353
EP  - 373
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am37-3-6/
DO  - 10.4064/am37-3-6
LA  - en
ID  - 10_4064_am37_3_6
ER  - 
%0 Journal Article
%A Shouquan Ma
%A Guixiang Xu
%T Global well-posedness and blow up for
 the nonlinear fractional beam equations
%J Applicationes Mathematicae
%D 2010
%P 353-373
%V 37
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/am37-3-6/
%R 10.4064/am37-3-6
%G en
%F 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) no. 3, pp. 353-373. doi: 10.4064/am37-3-6

Cité par Sources :