The existence of the global solutions to semilinear wave equations with a class of cubic nonlinearities in 2-dimensional space

摘要

This paper deals with the Cauchy problem of the semilinear wave equationwith a small initial data in 2-dimensional space. When the nonlinearity is cubic, wecan not expect the global existence of smooth solutions, in general. However, Godin [1]showed that if the nonlinearity has the null-form, the solution exists globally. In thispaper, we will show the global solvability for the other type of nonlinearities which doesnot have null-form.