Regularity and scattering for the wave equation with a critical nonlinear damping

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概要

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• We show that the nonlinear wave equation □u+ut3=0 is globally well-posed in radially symmetric Sobolev spaces Hkrad(R3)×Hk−1rad(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.

• 社団法人 日本数学会の論文
• 2009-04-01

著者

• Ugurlu Davut

  Abant Izzet Baysal University

• TODOROVA Grozdena

  University of Tennessee -Knoxville

• YORDANOV Borislav

  University of Tennessee -Knoxville

• Yordanov Borislav

  University of Tennessee

• Todorova Grozdena

  University of Tennessee

関連論文

• Regularity and scattering for the wave equation with a critical nonlinear damping
• Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

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