非线性对称双曲组的局部可解性

The Local Solvability for a Nonlinear Symmetric Hyperbolic System

本文定义并运用带参数仿微分算子工具(paradifferential operator)研究了一阶非线性对称双曲组Cauchy问题局部可解性.进一步表明:当s>n/2,解在H^s(Ω)中存在唯一,以及其奇性频率对初始条件的依赖性.

The Cauchy problem of a class of the nonlinear symmetric hyperbolic system are considered, where Aj. f are smooth function of (t,u):S is an integer. Aj are symmetric m×m matrices, u=(u1…,um)Tparaproduct and paradifferential operator with parameter t were defined. We got an energy estimate for the linear paradifferential Symmetric hyperbolic system and then proved that there exist T0>0 such that the problem has a unigue generalized solution u(x,t) ∈ C([0,T0],HS-1).