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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 partial differential equations (PDEs). A key feature of a solution to a linear dispersive PDE is that it spreads out and decays, while keeping a constant L^2 norm for all times. More specifically, we will study the long-time behavior of non-linear systems involving Dirac, Wave, and Schrödinger equations in a setting where dispersive and nonlinear effects are of the same strength. Furthermore, the long-time behavior of solutions to stochastic nonlinear dispersive PDEs will be analyzed. In a parallel line of research, new estimates related to the Fourier restriction theory in harmonic analysis will be derived.


Recent Preprints:

26009 Martin Spitz, Deng Zhang, Zhenqi Zhao PDF

The stochastic Zakharov system in dimension d≥4: Local well-posedness and regularization by noise for scattering

Project: A1

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The stochastic Zakharov system in dimension d≥4: Local well-posedness and regularization by noise for scattering


Authors: Martin Spitz, Deng Zhang, Zhenqi Zhao Projects: A1
Submission Date: 14.04.2026 Submitter: Sebastian Herr
Download: PDF Link: 26009

26004 Sebastian Herr, Christopher Maulén Marchant, Claudio Muñoz PDF

Decay of solutions of nonlinear dirac equations: the 2D case

Project: A1

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Decay of solutions of nonlinear dirac equations: the 2D case


Authors: Sebastian Herr, Christopher Maulén Marchant, Claudio Muñoz Projects: A1
Submission Date: 04.02.2026 Submitter: Matthias Erbar
Download: PDF Link: 26004

25042 Christopher Maulén Marchant, Claudio Muñoz, Felipe Poblete PDF

Decay of small energy solutions in the ABCD Boussinesq model under the influence of an uneven bottom

Project: A1

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Decay of small energy solutions in the ABCD Boussinesq model under the influence of an uneven bottom


Authors: Christopher Maulén Marchant, Claudio Muñoz, Felipe Poblete Projects: A1
Submission Date: 18.07.2025 Submitter: Sebastian Herr
Download: PDF Link: 25042

25032 Martin Spitz, Deng Zhang, Zhenqi Zhao PDF

Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations

Project: A1

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Regularization by noise for the energy- and mass-critical nonlinear Schrödinger equations


Authors: Martin Spitz, Deng Zhang, Zhenqi Zhao Projects: A1
Submission Date: 08.05.2025 Submitter: Sebastian Herr
Download: PDF Link: 25032

25027 Sebastian Herr, Robert Schippa, Nikolay Tzvetkov PDF

Global results for weakly dispersive KP-II equations on the cylinder

Project: A1

To appear: Archive for Rational Mechanics and Analysis (2026)

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Global results for weakly dispersive KP-II equations on the cylinder


Authors: Sebastian Herr, Robert Schippa, Nikolay Tzvetkov Projects: A1
Submission Date: 16.04.2025 Submitter: Martina Hofmanová
Download: PDF Link: 25027
To appear: Archive for Rational Mechanics and Analysis (2026)

25025 Benjamin Gess, Sebastian Herr, Anne Dorothea Niesdroy PDF

Existence of martingale solutions to a stochastic kinetic model of chemotaxis

Project: A1, B8

Published: Nonlinear Differ. Equ. Appl. 33, no. 52 (2026)

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Existence of martingale solutions to a stochastic kinetic model of chemotaxis


Authors: Benjamin Gess, Sebastian Herr, Anne Dorothea Niesdroy Projects: A1, B8
Submission Date: 02.04.2025 Submitter: Matthias Erbar
Download: PDF Link: 25025
Published: Nonlinear Differ. Equ. Appl. 33, no. 52 (2026)

25019 Sebastian Herr, Christopher Maulén Marchant, Claudio Muñoz PDF

Decay of solutions of nonlinear Dirac equations

Project: A1

Published: Commun. Math. Phys. 407, no. 94 (2026)

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Decay of solutions of nonlinear Dirac equations


Authors: Sebastian Herr, Christopher Maulén Marchant, Claudio Muñoz Projects: A1
Submission Date: 10.03.2025 Submitter: Matthias Erbar
Download: PDF Link: 25019
Published: Commun. Math. Phys. 407, no. 94 (2026)

25005 Emanuela Gussetti, Martina Hofmanová PDF

Statistical solutions to the Schrödinger map equation in 1D, via the randomly forced Landau-Lifschitz-Gilbert equation

Project: A1, B7

Published: Communications in Partial Differential Equations 50, no. 10-12 (2025), 1291-1326

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Statistical solutions to the Schrödinger map equation in 1D, via the randomly forced Landau-Lifschitz-Gilbert equation


Authors: Emanuela Gussetti, Martina Hofmanová Projects: A1, B7
Submission Date: 29.01.2025 Submitter: Sebastian Herr
Download: PDF Link: 25005
Published: Communications in Partial Differential Equations 50, no. 10-12 (2025), 1291-1326

25003 Christopher Maulén Marchant, Claudio Muñoz PDF

On asymptotic stability of stable Good Boussinesq solitary waves

Project: A1

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On asymptotic stability of stable Good Boussinesq solitary waves


Authors: Christopher Maulén Marchant, Claudio Muñoz Projects: A1
Submission Date: 24.01.2025 Submitter: Sebastian Herr
Download: PDF Link: 25003

24057 Sebastian Herr, Michael Röckner, Martin Spitz, Deng Zhang PDF

The energy-critical stochastic zakharov system

Project: A1, B1

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The energy-critical stochastic zakharov system


Authors: Sebastian Herr, Michael Röckner, Martin Spitz, Deng Zhang Projects: A1, B1
Submission Date: 08.10.2024 Submitter: Vitali Wachtel
Download: PDF Link: 24057


All Publications of this Project


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