Global well-posedness and blow up for the nonlinear fractional beam equations

Volume 37 / 2010

Shouquan Ma, Guixiang Xu Applicationes Mathematicae 37 (2010), 353-373 MSC: Primary 35G25, 35B44. DOI: 10.4064/am37-3-6

Abstract

We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.

Authors

  • Shouquan MaGraduate School
    China Academy of Engineering Physics
    P.O. Box 2101
    Beijing, China, 100088
    e-mail
  • Guixiang XuInstitute of Applied Physics
    and Computational Mathematics
    P.O. Box 8009
    Beijing, China, 100088
    e-mail

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