Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on IR3 Academic Article uri icon

abstract

  • We consider the defocusing nonlinear wave equation of power-type on $mathbb{R}^3$. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of initial data of super-critical regularity which lead to global solutions. The proof is based upon Bourgain's high-low frequency decomposition and improved averaging effects for the free evolution of the randomized initial data.

published proceedings

  • COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

  • Luehrmann, J., & Mendelson, D.

citation count

  • 52

complete list of authors

  • Luehrmann, Jonas||Mendelson, Dana

publication date

  • January 2014