DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kwon, Soonsik | - |
dc.contributor.advisor | 권순식 | - |
dc.contributor.author | Seong, Kihoon | - |
dc.date.accessioned | 2023-06-22T19:33:46Z | - |
dc.date.available | 2023-06-22T19:33:46Z | - |
dc.date.issued | 2022 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=1007831&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/308551 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2022.8,[vi, 163 p. | - |
dc.description | ] | - |
dc.description.abstract | We study the transport properties of the Gibbs and Gaussian measures on functions/distributions under the flow of Hamiltonian PDEs. In Chapter 2 and 3, we consider the quasi-invariance of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fractional nonlinear Schrodinger equation. For the case of second-order dispersion or greater, we establish an optimal regularity result for the quasi-invariance of these Gaussian measures. Moreover, we obtain an explicit formula for the Radon-Nikodym derivative. In particular, as for the case of fourth-order dispersion, we extend the quasi-invariance results to Sobolev spaces of negative regularity. In Chapter 4, we study focusing Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. Using the variational formulation, we prove the non-normalizability of the Gibbs measure with a quartic interaction. We also present the construction of the focusing Gibbs measure with a cubic interaction and non-normalizability of the Gibbs measure for the two-dimensional Zakharov system. In Chapter 5, we consider the Gibbs dynamics for the Zakharov-Yukawa system on the two-dimensional torus T2, namely a Schrodinger-wave system with a Zakharov-type coupling. We construct the Gibbs measure in the weakly nonlinear coupling case and study the invariance of the Gibbs measure under the resulting dynamics. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Schrodinger equation▼aZakharov-Yukawa system▼aGibbs measure▼aGaussian measure▼ainvariant measure▼aquasi-invariant measure▼alog-correlated Gaussian field▼anon-normalizability | - |
dc.subject | 슈뢰딩거 방정식▼a자카로프-유카와 시스템▼a깁스 측도▼a가우시안 측도▼a불변 측도▼a준 불변 측도▼a로그 상관성을 가진 가우시안 필드▼a비정규화 | - |
dc.title | Transport properties of Gibbs and Gaussian measures under the flow of Hamiltonian PDEs | - |
dc.title.alternative | 깁스 그리고 가우시안 측도들의 해밀토니안 편미분 방정식들의 흐름에 따른 운송 성질들 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :수리과학과, | - |
dc.contributor.alternativeauthor | 성기훈 | - |
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