Global existence for rough solutions of a fourth-order nonlinear wave equation

Abstract

In this paper, we prove that the cubic fourth-order wave equation is globally well-posed in H s ( R n ) for s > min { n − 2 2 , n 4 } by following the Bourgain's Fourier truncation idea in Bourgain (1998) [2]. To avoid some troubles, we technically make use of the Strichartz estimate for low frequency part and high frequency part, respectively. As far as we know, this is the first result on the low regularity behavior of the fourth-order wave equation.