DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kwon, Soon-Sik | - |
dc.contributor.advisor | 권순식 | - |
dc.contributor.author | Kwak, Chul-Kwang | - |
dc.contributor.author | 곽철광 | - |
dc.date.accessioned | 2013-09-12T02:33:11Z | - |
dc.date.available | 2013-09-12T02:33:11Z | - |
dc.date.issued | 2012 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=509385&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/181587 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 수리과학과, 2012.8, [ ii, 54 p. ] | - |
dc.description.abstract | In this paper, we mainly prove that the following the fifth-order equation arising from the Korteweg-de Vries (KdV) hierarchy \begin{equation*} \begin{cases} \pt u + \px^5 u + c_1\px u\px^2 u + c_2u\px^3 u = 0 \qquad x,t \in \R \\ u(0,x) = u_0(x) \qquad u_0 \in H^s(\R) \end{cases} \end{equation*} is locall well-posed with initial data in $H^s(\R)$ for $s > \frac54$. \\ The method is a short time $X^{s,b}$ space, which is developed by Ionescu-Kenig-Tataru \cite{IKT} in the context of the KP-I equation. In addition, we use a weight on $X^{s,b}$ to reduce the contribution of high-low frequency interaction where the low frequency has large modulation in the proof of energy estimate. As an immediate result from a conservation law, we have the second equation in the KdV hierarchy, $$\partial_t u - \px^5 u -30u^2\px u + 20\px u\px^2 u + 10u\px^3u=0$$ is globally well-posed in $H^2$.\\ Moreover, we introduce the standard \emph{$X^{s,b}$ space} and counter-examples that the nonlinear estimates fails in the usual \emph{$X^{s,b}$ spaces}. We also prove that the KdV equation is locally well-posed with initial data in $H^s(\R)$ for $s > -\frac34$ by using the Picard iteration argument. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | b}$ space | - |
dc.subject | local well-posedness | - |
dc.subject | the KdV equation | - |
dc.subject | b}$ 함수 공간 | - |
dc.subject | 해의 존재성 | - |
dc.subject | KdV 방정식 | - |
dc.subject | 5계 KdV 방정식 | - |
dc.subject | the fifth-order KdV | - |
dc.title | Local well-posedness of the fifth-order KdV equations for rough data using short time $X^{s,b}$ structures | - |
dc.title.alternative | $X^{s,b}$ 구조를 이용한 5계 KdV 방정식의 해의 존재성 연구 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 509385/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020104246 | - |
dc.contributor.localauthor | Kwon, Soon-Sik | - |
dc.contributor.localauthor | 권순식 | - |
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