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April, 2009 Regularity and scattering for the wave equation with a critical nonlinear damping
Grozdena TODOROVA, Davut UĞURLU, Borislav YORDANOV
J. Math. Soc. Japan 61(2): 625-649 (April, 2009). DOI: 10.2969/jmsj/06120625


We show that the nonlinear wave equation u+ut3=0 is globally well-posed in radially symmetric Sobolev spaces Hradk(R3)× Hradk-1(R3) for all integers k>2. This partially extends the well-posedness in Hk(R3)× Hk-1(R3) for all k [1,2], established by Lions and Strauss[12]. As a consequence we obtain the global existence of C solutions with radial C0 data. The regularity problem requires smoothing and non-concentration estimates in addition to standard energy estimates, since the cubic damping is critical when k=2. We also establish scattering results for initial data (u,ut)|t=0 in radially symmetric Sobolev spaces.


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Grozdena TODOROVA. Davut UĞURLU. Borislav YORDANOV. "Regularity and scattering for the wave equation with a critical nonlinear damping." J. Math. Soc. Japan 61 (2) 625 - 649, April, 2009.


Published: April, 2009
First available in Project Euclid: 13 May 2009

zbMATH: 1180.35363
MathSciNet: MR2532904
Digital Object Identifier: 10.2969/jmsj/06120625

Primary: 35L15 , 35L70
Secondary: 37L05

Keywords: nonlinear damping , regularity , wave equation

Rights: Copyright © 2009 Mathematical Society of Japan


Vol.61 • No. 2 • April, 2009
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