Scattering for Radial, Bounded Solutions of Focusing Supercritical Wave Equations

作者：Duyckaerts Thomas^*; Kenig Carlos; Merle Frank

来源：International Mathematics Research Notices, 2014, 2014(1): 224-258.

DOI：10.1093/imrn/rns227

In this paper, we consider the wave equation in space dimension 3 with an energy-supercritical, focusing nonlinearity. We show that any radial solution of the equation which is bounded in the critical Sobolev space is globally defined and scatters to a linear solution. As a consequence, finite time blow-up solutions have critical Sobolev norm converging to infinity (along some sequence of times). The proof relies on the compactness/rigidity method, pointwise estimates on compact solutions obtained by the last two authors, and channels of energy arguments used by the authors in previous works on the energy-critical equation.

• 出版日期2014