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Project A1: Nonlinear interactions of rough waves


Principal Investigator(s)
Sebastian Herr
Visitor(s)
Currently no visitors.

Summary:

This project is devoted to the mathematical analysis of nonlinear dispersive evolution equations and systems. A key feature of a solution to a linear dispersive equation with square-integrable initial data is that it spreads out and decays, while keeping a constant mass for all times. For instance, we will address questions on the long-time behavior of non-linear Dirac equations, the Dirac-Klein-Gordon system, the Dirac-Maxwell system, and the Zakharov system in a setting where dispersive and nonlinear effects are of the same strength. In a parallel line of research, new estimates related to the Fourier restriction theory in harmonic analysis will be derived.


Recent Preprints:

20093 Sebastian Herr, Shinya Kinoshita PDF

The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity

Project: A1

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The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity


Authors: Sebastian Herr, Shinya Kinoshita Projects: A1
Submission Date: 25.08.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20093

20055 Timothy Candy PDF

A note on bilinear wave-Schrödinger interactions

Project: A1

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A note on bilinear wave-Schrödinger interactions


Authors: Timothy Candy Projects: A1
Submission Date: 25.05.2020 Submitter: Sebastian Herr
Download: PDF Link: 20055

20054 Timothy Candy, Sebastian Herr, Kenji Nakanishi PDF

Global wellposedness for the energy-critical Zakharov system below the ground state

Project: A1

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Global wellposedness for the energy-critical Zakharov system below the ground state


Authors: Timothy Candy, Sebastian Herr, Kenji Nakanishi Projects: A1
Submission Date: 21.05.2020 Submitter: Alexander Grigor'yan
Download: PDF Link: 20054

20038 Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov, Yuzhao Wang PDF

Stochastic quantization of Liouville conformal field theory

Project: A1

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Stochastic quantization of Liouville conformal field theory


Authors: Tadahiro Oh, Tristan Robert, Nikolay Tzvetkov, Yuzhao Wang Projects: A1
Submission Date: 14.04.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20038

20012 Sebastian Herr, Shinya Kinoshita PDF

Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher

Project: A1

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Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher


Authors: Sebastian Herr, Shinya Kinoshita Projects: A1
Submission Date: 27.01.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20012

19107 Timothy Candy, Sebastian Herr, Kenji Nakanishi PDF

The Zakharov system in dimension d ≥ 4

Project: A1

To appear: Journal of the European Mathematical Society

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The Zakharov system in dimension d ≥ 4


Authors: Timothy Candy, Sebastian Herr, Kenji Nakanishi Projects: A1
Submission Date: 16.12.2019 Submitter: Michael Röckner
Download: PDF Link: 19107
To appear: Journal of the European Mathematical Society

19017 Shinya Kinoshita PDF

Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D

Project: A1

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Global Well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D


Authors: Shinya Kinoshita Projects: A1
Submission Date: 07.05.2019 Submitter: Sebastian Herr
Download: PDF Link: 19017

18079 Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto PDF

Well-posedness for KdV-type equations with quadratic nonlinearity

Project: A1

Published: Journal of Evolution Equations (2019), DOI: 10.1007/s00028-019-00540-6: 1–25

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Well-posedness for KdV-type equations with quadratic nonlinearity


Authors: Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto Projects: A1
Submission Date: 27.12.2018 Submitter: Sebastian Herr
Download: PDF Link: 18079
Published: Journal of Evolution Equations (2019), DOI: 10.1007/s00028-019-00540-6: 1–25

18056 Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto PDF

Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data

Project: A1

Published: Annales Henri Poincaré 21 (2020), 2611–2636

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Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data


Authors: Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto Projects: A1
Submission Date: 21.11.2018 Submitter: Sebastian Herr
Download: PDF Link: 18056
Published: Annales Henri Poincaré 21 (2020), 2611–2636

18024 Timothy Candy, Sebastian Herr PDF

On the division problem for the wave maps equation

Project: A1

Published: Annals of PDE 4 (2018), 17: 1–61

Notes: doi 10.1007/s40818-018-0054-z

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On the division problem for the wave maps equation


Authors: Timothy Candy, Sebastian Herr Projects: A1
Submission Date: 06.07.2018 Submitter: Michael Röckner
Download: PDF Link: 18024
Published: Annals of PDE 4 (2018), 17: 1–61
Notes: doi 10.1007/s40818-018-0054-z



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