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Project A1: Nonlinear interactions of rough waves


Principal Investigator(s)
Sebastian Herr

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:

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

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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

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

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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

18024 Timothy Candy, Sebastian Herr PDF

On the division problem for the wave maps equation

Project: A1

Published: Annals of PDE 4, no. 2 (2018), 17

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, no. 2 (2018), 17
Notes: doi 10.1007/s40818-018-0054-z

18014 Sebastian Herr, Michael Röckner, Deng Zhang PDF

Scattering for Stochastic Nonlinear Schrödinger Equations

Project: A1, B1

Published: Communications in Mathematical Physics 368, no. 2 (2019), 843-884

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Scattering for Stochastic Nonlinear Schrödinger Equations


Authors: Sebastian Herr, Michael Röckner, Deng Zhang Projects: A1, B1
Submission Date: 30.04.2018 Submitter: Alexander Grigor'yan
Download: PDF Link: 18014
Published: Communications in Mathematical Physics 368, no. 2 (2019), 843-884

18010 Timothy Candy, Christopher Kauffman, Hans Lindblad PDF

Asymptotic behavior of the Maxwell-Klein-Gordon system

Project: A1

Published: Commun. Math. Phys. (2019), 1-34

Notes: https://doi.org/10.1007/s00220-019-03285-y

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Asymptotic behavior of the Maxwell-Klein-Gordon system


Authors: Timothy Candy, Christopher Kauffman, Hans Lindblad Projects: A1
Submission Date: 11.04.2018 Submitter: Sebastian Herr
Download: PDF Link: 18010
Published: Commun. Math. Phys. (2019), 1-34
Notes: https://doi.org/10.1007/s00220-019-03285-y

17021 Timothy Candy, Sebastian Herr PDF

Conditional large initial data scattering results for the Dirac-Klein-Gordon system

Project: A1

Published: Forum of Mathematics, Sigma 6, no. E9 (2018)

Notes: doi:10.1017/fms.2018.8

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Conditional large initial data scattering results for the Dirac-Klein-Gordon system


Authors: Timothy Candy, Sebastian Herr Projects: A1
Submission Date: 28.09.2017 Submitter: Michael Baake
Download: PDF Link: 17021
Published: Forum of Mathematics, Sigma 6, no. E9 (2018)
Notes: doi:10.1017/fms.2018.8

17020 Timothy Candy, Sebastian Herr PDF

On the Majorana condition for nonlinear Dirac systems

Project: A1

Published: Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 35, no. 6 (2018), 1707–1717

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On the Majorana condition for nonlinear Dirac systems


Authors: Timothy Candy, Sebastian Herr Projects: A1
Submission Date: 28.09.2017 Submitter: Michael Baake
Download: PDF Link: 17020
Published: Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire 35, no. 6 (2018), 1707–1717

17004 Timothy Candy PDF

Multi-scale bilinear restriction estimates for general phases

Project: A1

To appear: Mathematische Annalen (2019)

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Multi-scale bilinear restriction estimates for general phases


Authors: Timothy Candy Projects: A1
Submission Date: 28.07.2017 Submitter: Sebastian Herr
Download: PDF Link: 17004
To appear: Mathematische Annalen (2019)



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