Global existence for systems of nonlinear wave equations in 3D with multiple speeds. (English) Zbl 1002.35091
The authors study the Cauchy problem for coupled systems of quasilinear wave equations in three space dimensions with different propagation speeds. An additional set of weighted \(L^2\) estimates is used to obtain a viable \(L^\infty-L^2\) estimate for solutions. The results are applied to nondivergence form nonlinearities which may contain both spatial and temporal derivatives and satisfy the null condition.
Reviewer: Luis Vazquez (Madrid)
MSC:
35L70 | Second-order nonlinear hyperbolic equations |
35L55 | Higher-order hyperbolic systems |
35L15 | Initial value problems for second-order hyperbolic equations |