摘要
In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut + uxxx + λH(uxx) + u2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hrs(R) for 34 < r ≤ 2, b > r1 and s ≥ s(r) = 21 21r. In particular, for r = 2, we reobtain the result in [3].
In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut ＋ uxxx ＋ λH（uxx） ＋ u^2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hr^s（R） for 4/3 〈r≤2, b〉1/r and s≥s（r）= 1/2- 1/2r. In particular, for r = 2, we reobtain the result in [3].
基金
the Natural Science Foundation of Zhejiang Province （No. Y6080388）
the Science and Technology Research Foundation of Zhejiang Ocean University （Nos. X08M014
X08Z04）.
