Maximizers for the Strichartz Inequalities for the wave equation
By Aynur Bulut. Differential and Integral Equations, 2009
67 citations recorded by the source corpus.
We prove the existence of maximizers for Strichartz inequalities for the wave equation in dimensions $d\geq 3$. Our approach follows the scheme given by Shao, which obtains the existence of maximizers in the context of the Schr\"odinger equation. The main tool that we use is the linear profile decomposition for the wave equation which we prove in $\mathbb{R}^d$, $d\geq 3$, extending the profile decomposition result of Bahouri and Gerard, previously obtained in $\mathbb{R}^3$.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cee6236b4da0d04dceb363160ae9adae94920a02
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
- Aynur Bulut
- Carlos E. Kenig
- Nicola Visciglia
- Hao Jia
- Xiaoyi Zhang
- Natavsa Pavlovi'c
- Dong Li
- M. Czubak
In Mathematical Physics
- Aynur Bulut
- Carlos E. Kenig
- Hao Jia
- Nicola Visciglia
- Xiaoyi Zhang
- Luis Vega
- B. Dodson
- Natavsa Pavlovi'c
Citations in the corpus
- Asymptotic decomposition for semilinear Wave and equivariant wave map equations (2015, methodology): “Next we use the profile decompositions introduced in the context of wave equations by Bahouri and Gerard [1], (see also [2] in the case of R1+6).”
- Global Well-Posedness and Scattering for the Defocusing Energy-Supercritical Cubic Nonlinear Wave Equation (2010, methodology): “For more details, we refer the reader to [1, 2].”
- Existence of maximizers for Sobolev–Strichartz inequalities (2011, methodology): “We also mention the papers by Shao [14] for the Schödinger equation and by Bulut [3] for the wave equation, in which the existence of maximizers for anisotropic Strichartz estimates in spaces LptL q x, for general couples (p, q), is also proved.”
- Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions (2009, methodology): “We expect that the stability result of this paper combined with a modification of the profile decomposition for the linear wave equation, that was for d = 3 obtained by Bahouri and Gérard [1] and extended to high dimensions d > 3 by Bulut [3], implies that the dichotomy result of Kenig and Merle [17”