We consider systems of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the classical solution under a new structural condition related to the weak null condition. For two-component systems satisfying this condition, we also observe a new kind of asymptotic behavior: Only one component is dissipated and the other one behaves like a free solution in the large time.
- Pub Date:
- May 2012
- Mathematics - Analysis of PDEs;
- 32 pages. Statements of main theorems have been changed in order to treat more general situation. Accordingly, the title and the abstarct have also been modified