High frequency approximation of solutions to critical nonlinear wave equations
1999; Johns Hopkins University Press; Volume: 121; Issue: 1 Linguagem: Inglês
10.1353/ajm.1999.0001
ISSN1080-6377
AutoresHajer Bahouri, Patrick Gérard,
Tópico(s)Advanced Harmonic Analysis Research
ResumoThis work is devoted to the description of bounded energy sequences of solutions to the equation (1) □ u + | u | 4 = 0 in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], up to remainder terms small in energy norm and in every Strichartz norm. The proof relies on scattering theory for (1) and on a structure theorem for bounded energy sequences of solutions to the linear wave equation. In particular, we infer the existence of an a priori estimate of Strichartz norms of solutions to (1) in terms of their energy.
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