Life-span of classical solutions to two dimensional fully nonlinear wave equations

摘要

In two-space-dimensional case, we get the lower bound of the life-span of classical solutions to the Cauchy problem with small initial data for fully nonlinear wave equations of the form square u = F(u,Du,DxDu) in which F((lambda) over cap) = O(vertical bar(lambda) over cap vertical bar(3)) in a neighbourhood of (lambda) over cap = 0, and partial derivative F-3(u)(0,0,0) = O. For the purpose, some refined estimates including Strichartz estimates are needed in the paper. (C) 2016 Elsevier Inc. All rights reserved.