中国科学院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

偏微分方程研讨班

报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（1）

时  间：2024.9.16  9：00-9：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（2）

时  间：2024.9.16  10：00-10：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（3）

时  间：2024.9.17  9：00-9：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（4）

时  间：2024.9.17  10：00-10：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（5）

时  间：2024.9.19  9：00-9：50

地  点：N820 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（6）

时  间：2024.9.19  10：00-10：50

地  点：N820 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（7）

时  间：2024.9.20  9：00-9：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.

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报告人：Prof.Herbert Koch

(University of Bonn, Germany)

题  目： The Korteweg-de Vries Hierarchy at Low Regularity（8）

时  间：2024.9.20  10：00-11：50

地  点：N913 Zoom meeting: 878 4974 2364 Code: AMSS2024

摘  要：The Korteweg-de Vries hierarchy and its relation to its Lax operator is discussed. In particular this leads to a relation between the Gardner hierarchy and the Korteweg-Vries hierarchy by the Miura map related to a factorization of the Lax operator.

The study of the low regularity Cauchy problem is based on estimates for the generating functions of the Korteweg-de Vries and the Gardner Hamiltonians, which allow to implement the seminal approach of Harrop-Griffith, Killip and Visan to prove well-posedness of the whole Gardner hierarchy in , and hence of the Korteweg-de Vries hierarchy in low regularity.