Project A1: Nonlinear interactions of rough waves
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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:
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
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25027
Sebastian Herr, Robert Schippa, Nikolay Tzvetkov PDF
Global results for weakly dispersive KP-II equations on the cylinder
Project:
A1
X
Global results for weakly dispersive KP-II equations on the cylinder
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25025
Benjamin Gess, Sebastian Herr, Anne Dorothea Niesdroy PDF
Existence of martingale solutions to a stochastic kinetic model of chemotaxis
Project:
A1, B8
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Existence of martingale solutions to a stochastic kinetic model of chemotaxis
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25019
Sebastian Herr, Christopher Maulén Marchant, Claudio Muñoz PDF
Decay of solutions of nonlinear Dirac equations
Project:
A1
X
Decay of solutions of nonlinear Dirac equations
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25003
Christopher Maulén Marchant, Claudio Muñoz PDF
On asymptotic stability of stable Good Boussinesq solitary waves
Project:
A1
X
On asymptotic stability of stable Good Boussinesq solitary waves
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24077
Sebastian Herr, Michael Röckner, Martin Spitz, Deng Zhang PDF
The energy-critical stochastic zakharov system
Project:
A1, B1
X
The energy-critical stochastic zakharov system
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24069
L’ubomír Baňas, Sebastian Herr PDF
Numerical approximation of bi-harmonic wave maps into spheres
Project:
A1, B3
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Numerical approximation of bi-harmonic wave maps into spheres
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24053
Sebastian Herr, Robert Schippa, Nikolay Tzvetkov PDF
The Cauchy problem for the periodic Kadomtsev--Petviashvili--II equation below $L^2$
Project:
A1
X
The Cauchy problem for the periodic Kadomtsev--Petviashvili--II equation below $L^2$
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24044
Shinya Kinoshita PDF
Well-posedness for the Cauchy Problem of the Modified Zakharov-Kuznetsov Equation
Project:
A1
Published: Funkcialaj Ekvacioj 65, no. 2 (2022), 139-158
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Well-posedness for the Cauchy Problem of the Modified Zakharov-Kuznetsov Equation
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24042
Sebastian Herr, Mihaela Ifrim, Martin Spitz PDF
Modified scattering for the three dimensional Maxwell-Dirac system
Project:
A1
X
Modified scattering for the three dimensional Maxwell-Dirac system
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All Publications of this Project
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