广义KdV--BO方程的Cauchy问题的局部适定性的改进结果

Improved Local Wellposedness of Cauchy Problem for Generalized KdV-BO Equation

中文关键词:  广义KdV--BO方程  Cauchy问题  局部适定.

英文关键词:KdV-BO equation  Cauchy problem  local wellposedness.

中文摘要:

      本文证明了广义KdV--BO方程:$u_t u_{xxx} \lambda{\cal H}(u_{xx}) u^2u_x = 0$, $ x\in R$, $t\ge 0$的Cauchy问题在$\widehat{H^s_r} (R)$上局部适定,其中$\frac 43 \frac 1 r$, $s \ge s(r)=\frac 12-\frac 1{2r}$.特别地,当$r=2$时,对应[3]的结果.

英文摘要:

      In this paper we prove that the Cauchy problem associated with the generalized KdV--BO equation $u_t u_{xxx} \lambda{\cal H}(u_{xx}) u^2u_x=0$, $x\in R$, $t\ge 0$ is locally wellposed in $\widehat{H^s_r} (R)$ for $\frac43 \frac 1 r$ and $s \ge s(r)=\frac 12-\frac 1{2r}$. In particular, for $r=2$, we reobtain the result in [3].