| 广义KdV--BO方程的Cauchy问题的局部适定性的改进结果 |
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| 引用本文： | 赵向青,郭艾.广义KdV--BO方程的Cauchy问题的局部适定性的改进结果[J].数学研究及应用,2009,29(2):371-375. |
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| 作者姓名： | 赵向青 郭艾 |
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| 作者单位： | 浙江海洋学院数学系, 浙江 舟山 316000;华南理工大学数学科学学院, 广东 广州 510640 |
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| 基金项目： | 浙江省自然科学基金(No.Y6080388); 浙江海洋学院科研基金(Nos.X08M014; X08Z04). |
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| 摘 要： | 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].
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| 关 键 词： | 广义KdV-BO方程 Cauchy问题 局部适定性 改进结果 |
| 收稿时间： | 2006/12/4 0:00:00 |
| 修稿时间： | 2007/10/28 0:00:00 |
Improved Local Wellposedness of Cauchy Problem for Generalized KdV-BO Equation |
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| ZHAO Xiang Qing and GUO Ai.Improved Local Wellposedness of Cauchy Problem for Generalized KdV-BO Equation[J].Journal of Mathematical Research with Applications,2009,29(2):371-375. |
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| Authors: | ZHAO Xiang Qing and GUO Ai |
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| Institution: | Department of Mathematics, Zhejiang Ocean University, Zhejiang 316000, China;School of Mathematical Sciences, South China University of Technology, Guangdong 510640, China |
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| Abstract: | 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]. |
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| Keywords: | KdV-BO equation Cauchy problem local wellposedness |
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