강연 / 세미나
PDE and Applied Analysis Seminar
| 분야Field | |||
|---|---|---|---|
| 날짜Date | 2023-05-18 ~ 2023-05-18 | 시간Time | 16:00 ~ 17:00 |
| 장소Place | Online | 초청자Host | |
| 연사Speaker | Kihyun Kim | 소속Affiliation | IHES |
| TOPIC | PDE and Applied Analysis Seminar | ||
| 소개 및 안내사항Content | Abstract: We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.
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| 학회명Field | PDE and Applied Analysis Seminar | ||
|---|---|---|---|
| 날짜Date | 2023-05-18 ~ 2023-05-18 | 시간Time | 16:00 ~ 17:00 |
| 장소Place | Online | 초청자Host | |
| 소개 및 안내사항Content | Abstract: We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.
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| 성명Field | PDE and Applied Analysis Seminar | ||
|---|---|---|---|
| 날짜Date | 2023-05-18 ~ 2023-05-18 | 시간Time | 16:00 ~ 17:00 |
| 소속Affiliation | IHES | 초청자Host | |
| 소개 및 안내사항Content | Abstract: We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.
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| 성명Field | PDE and Applied Analysis Seminar | ||
|---|---|---|---|
| 날짜Date | 2023-05-18 ~ 2023-05-18 | 시간Time | 16:00 ~ 17:00 |
| 호실Host | 인원수Affiliation | Kihyun Kim | |
| 사용목적Affiliation | 신청방식Host | IHES | |
| 소개 및 안내사항Content | Abstract: We consider the long time dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) within equivariant symmetry. Being a gauged 2D cubic nonlinear Schrödinger equation (NLS), (CSS) is L2-critical and has pseudoconformal invariance and solitons. However, there are two distinguished features of (CSS), the self-duality and non-locality, which make the long time dynamics of (CSS) surprisingly rigid. For instance, (i) any finite energy spatially decaying solutions to (CSS) decompose into at most one(!) modulated soliton and a radiation. Moreover, (ii) in the high equivariance case (i.e., the equivariance index ≥ 1), any smooth finite-time blow-up solutions even have a universal blow-up speed, namely, the pseudoconformal one. We explore this rigid dynamics using modulation analysis, combined with the self-duality and non-locality of the problem.
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Admin
·
2023-05-16 17:58 ·
조회 113 
