Random data Cauchy theory for supercritical wave equations I: local theory
By Nicolas Burq, Nikolay Tzvetkov. 2007
344 citations recorded by the source corpus.
We study the local existence of strong solutions for the cubic nonlinear wave equation with data in Hs(M), s<1/2, where M is a three dimensional compact Riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in Hs(M), where s≥1/4 in the case of a boundary less manifold and s≥8/21 in the case of a manifold with boundary.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c6ccd420ac2fda7093585ac589da63b63c8f3cfd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Gigliola Staffilani
- Andrea R. Nahmod
- Luc Rey-Bellet
- Tadahiro Oh
- D. Tataru
- Nikolay Tzvetkov
- Terence Tao
- Luc Molinet
In Control and Systems Engineering
- Tadahiro Oh
- Luc Rey-Bellet
- Gigliola Staffilani
- Andrea R. Nahmod
- Monica Visan
- Terence Tao
- D. Tataru
- Luc Molinet
In Mathematical Physics
- Gigliola Staffilani
- Andrea R. Nahmod
- Tadahiro Oh
- Luc Rey-Bellet
- D. Tataru
- Oana Pocovnicu
- Terence Tao
- James E. Colliander
Citations in the corpus
- Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\"odinger equation below the energy space (2013, background): “In the case of the ball or the sphere, if one restricts to the radial case then constructions of invariant measures are possible as in [35, 12, 20, 21, 6, 7, 8].”
- INVARIANT WEIGHTED WIENER MEASURES AND ALMOST SURE GLOBAL WELL-POSEDNESS FOR THE PERIODIC DERIVATIVE NLS. (2010, background): “Tzvetkov [12, 13] for subcubic and subquartic radial nonlinear wave equations on 3d ball, N.”