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Project A1.1: Nonlinear interactions of rough waves


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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:

21037 Sebastian Herr, Isao Kato, Shinya Kinoshita, Martin Spitz PDF

Local well-posedness of a system describing laser-plasma interactions

Project: A1

Published: Vietnam J. Math. 51 (2023), 759–770

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Local well-posedness of a system describing laser-plasma interactions

Authors: Sebastian Herr, Isao Kato, Shinya Kinoshita, Martin Spitz Projects: A1
Submission Date: 05.05.2021 Submitter: Martina Hofmanová
Download: PDF Link: 21037
Published: Vietnam J. Math. 51 (2023), 759–770
21035 Tristan Robert PDF

Invariant Gibbs measure for a Schrodinger equation with exponential nonlinearity

Project: A1

Published: Journal of Functional Analysis 287 (2024), Article number 110592

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Invariant Gibbs measure for a Schrodinger equation with exponential nonlinearity

Authors: Tristan Robert Projects: A1
Submission Date: 30.04.2021 Submitter: Sebastian Herr
Download: PDF Link: 21035
Published: Journal of Functional Analysis 287 (2024), Article number 110592
20123 Martin Spitz PDF

Randomized final-state problem for the Zakharov system in dimension three

Project: A1

Published: Communications in Partial Differential Equations 47, no. 2 (2022), 346–377

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Randomized final-state problem for the Zakharov system in dimension three

Authors: Martin Spitz Projects: A1
Submission Date: 30.12.2020 Submitter: Sebastian Herr
Download: PDF Link: 20123
Published: Communications in Partial Differential Equations 47, no. 2 (2022), 346–377
20093 Sebastian Herr, Shinya Kinoshita PDF

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

Project: A1

Published: Journal of Evolution Equations 21 (2021), 2105-2121

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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
Published: Journal of Evolution Equations 21 (2021), 2105-2121
20055 Timothy Candy PDF

A note on bilinear wave-Schrödinger interactions

Project: A1

Published: 2019-20 MATRIX Annals. 4 (2022), 537-549

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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
Published: 2019-20 MATRIX Annals. 4 (2022), 537-549
20054 Timothy Candy, Sebastian Herr, Kenji Nakanishi PDF

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

Project: A1

Published: Advances in Mathematics 384, Article ID 107746 (2021), 57 pp.

Notes: DOI: 10.1016/j.aim.2021.107746

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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
Published: Advances in Mathematics 384, Article ID 107746 (2021), 57 pp.
Notes: DOI: 10.1016/j.aim.2021.107746
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

Published: Annales de l'Institut Fourier 73, no. 3 (2023), 1203-1267

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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
Published: Annales de l'Institut Fourier 73, no. 3 (2023), 1203-1267
19107 Timothy Candy, Sebastian Herr, Kenji Nakanishi PDF

The Zakharov system in dimension d ≥ 4

Project: A1

Published: J. Eur. Math. Soc. (JEMS) 25, no. 8 (2023), 3177–3228

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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
Published: J. Eur. Math. Soc. (JEMS) 25, no. 8 (2023), 3177–3228
19017 Shinya Kinoshita PDF

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

Project: A1

To appear: Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire (2020)

Notes: DOI: 10.1016/j.anihpc.2020.08.003

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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
To appear: Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire (2020)
Notes: DOI: 10.1016/j.anihpc.2020.08.003

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