Geodesic
Construction of two-bubble solutions for some energy-critical wave equations
Jendrej, Jacek1
1CMLS, École polytechnique, CNRS, Université Paris-Saclay 91128 Palaiseau Cedex France
Séminaire Laurent Schwartz — EDP et applications (2015-2016), Talk no. 21, 10 p.

See the original proceeding notice from the Numdam source

We present a construction of pure two-bubbles for some energy-critical wave equations, that is solutions which in one time direction approach a superposition of two stationary states both centered at the origin, but asymptotically decoupled in scale. Our solution exists globally, with one bubble at a fixed scale and the other concentrating in infinite time, with an error tending to 0 in the energy space. We treat the cases of the power nonlinearity in space dimension 6, the radial Yang-Mills equation and the equivariant wave maps equation with equivariance class k≥3. The concentration speed of the second bubble is exponential for the first two models and a power function in the last case.

Published online:
DOI: 10.5802/slsedp.90

Jendrej, Jacek  1

1 CMLS, École polytechnique, CNRS, Université Paris-Saclay 91128 Palaiseau Cedex France 
Jendrej, Jacek. Construction of two-bubble solutions for some energy-critical wave equations. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Talk no. 21, 10 p.. doi: 10.5802/slsedp.90
@article{SLSEDP_2015-2016____A21_0,
     author = {Jendrej, Jacek},
     title = {Construction of two-bubble solutions for some energy-critical wave equations},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:21},
     pages = {1--10},
     year = {2015-2016},
     publisher = {Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique},
     doi = {10.5802/slsedp.90},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/slsedp.90/}
}
TY  - JOUR
AU  - Jendrej, Jacek
TI  - Construction of two-bubble solutions for some energy-critical wave equations
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:21
PY  - 2015-2016
SP  - 1
EP  - 10
PB  - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique
UR  - http://geodesic.mathdoc.fr/articles/10.5802/slsedp.90/
DO  - 10.5802/slsedp.90
LA  - en
ID  - SLSEDP_2015-2016____A21_0
ER  - 
%0 Journal Article
%A Jendrej, Jacek
%T Construction of two-bubble solutions for some energy-critical wave equations
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:21
%D 2015-2016
%P 1-10
%I Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique
%U http://geodesic.mathdoc.fr/articles/10.5802/slsedp.90/
%R 10.5802/slsedp.90
%G en
%F SLSEDP_2015-2016____A21_0

Cited by Sources: