Kawahara-BO方程Cauchy问题的局部可解性

Local solvability of Cauchy problem for the Kawahara-BO equation

研究Kawahara-BO方程在低则Sobolev间H^r上的局部适定性和极限行为,证明了:当r>-7/5时,对任意的初始值u_0∈H^r,Kawahara-BO方程的Cauchy问题存在唯一的解u∈C([0,T],H^r)∩X^(r,s);当BO项系数λ趋向于0时,Kawahara-BO方程的解收敛到Kawahara方程的解.

The local well-posedness in low regularity Sobolev space H^T and the limit behavior of Kawahara-BO equation are studied. In fact, it is proved that if r〉-5-7,then of any initial value u0∈H^T,the Cauchy problem of Kawahara-BO admits a unique solution u∈C（[0,T]H^T）∩X^T,S;and when the ceofficient of BO term λ converges to 0, the solution of Kawahara-BO equation converges to that of Kawahara equation.