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Project A1: Nonlinear interactions of rough waves.

Principal Investigator(s)
Sebastian Herr

Investigator(s)
Anne Dorothea Niesdroy
Marc Rouveyrol
Martin Spitz

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:

26014 Anne Dorothea Niesdroy PDF

Global well-posedness of the Boltzmann equation via bilinear estimates

Project: A1

Global well-posedness of the Boltzmann equation via bilinear estimates

Authors:	Anne Dorothea Niesdroy	Projects:	A1
Submission Date:	14.07.2026	Submitter:	Sebastian Herr
Download:	PDF	Link:	26014

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

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

Published: SIAM Journal of Mathematical Analysis (accepted)

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
Published:	SIAM Journal of Mathematical Analysis (accepted)

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

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

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

Published: Archive for Rational Mechanics and Analysis 250, no. 46 (2026)

Notes: https://doi.org/10.1007/s00205-026-02208-1

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
Published:	Archive for Rational Mechanics and Analysis 250, no. 46 (2026)
Notes:	https://doi.org/10.1007/s00205-026-02208-1

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)

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)

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

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

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

All Publications of this Project

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