Energy partition for the linear radial wave equation

By Raphael Cote, Carlos E. Kenig, Wilhelm Schlag. 2012

56 citations recorded by the source corpus.

We consider the radial free wave equation in all dimensions and derive asymptotic formulas for the space partition of the energy, as time goes to infinity. We show that the exterior energy estimate, which Duyckaerts et al. obtained in odd dimensions (Duyckaerts et al., J Eur Math Soc 13:533–599, 2011; J Eur Math Soc, 2013) fails in even dimensions. Positive results for restricted classes of data are obtained.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fbb2d95debf1c2de653c8dcc4b27af204a31479d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Raphael Cote
2. Hao Jia
3. Carlos E. Kenig
4. Felipe Linares
5. Jean-Claude Saut
6. Tai-Peng Tsai

In Mathematical Physics

1. Raphael Cote
2. Hao Jia
3. Carlos E. Kenig
4. F. Merle
5. Aynur Bulut
6. Gunther Uhlmann
7. B. Dodson
8. Jean-Claude Saut

Citations in the corpus

• Soliton resolution for equivariant wave maps to the sphere (2013, background): “When g′(`) is odd, (LW`) corresponds to a wave equation in R with d ≡ 0 mod 4, and the linear estimate obtained in [8] in this case suffices to conclude.”
• Asymptotic decomposition for semilinear Wave and equivariant wave map equations (2015, background): “The following result from [12] says that essentially the free waves travel at unit speed.”