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Project B2: Stochastic partial differential equations with singular noise


Principal Investigator(s)
Rongchan Zhu
Xiangchan Zhu
Investigator(s)
Bingguang Chen
Huanyu Yang

Summary:

This project consists of two parts: (I) Strong approach to stochastic partial differential equations with singular noise: We plan to study global well-posedness, properties and approximations of stochastic partial differential equations with singular noise, based on the theory of regularity structures proposed by Hairer and on the paracontrolled distributions method introduced by Gubinelli, Imkeller and Perkowski. (II) Weak approach to stochastic partial differential equations with singular noise: The aim here is to construct and analyze weak solutions to singular stochastic partial differential equations by using both Dirichlet form theory and the energy solution method recently introduced by Gonçalves and Jara.


Recent Preprints:

18071 Kai Du, Xicheng Zhang PDF

Optimal gradient estimates of heat kernels of stable-like operators

Project: B1, B2

To appear: Proceedings of American Mathematics Society (2019)

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Optimal gradient estimates of heat kernels of stable-like operators


Authors: Kai Du, Xicheng Zhang Projects: B1, B2
Submission Date: 17.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18071
To appear: Proceedings of American Mathematics Society (2019)

18070 Xicheng Zhang, Guohuan Zhao PDF

Dirichlet problem for supercritical non-local operators

Project: B1, B2

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Dirichlet problem for supercritical non-local operators


Authors: Xicheng Zhang, Guohuan Zhao Projects: B1, B2
Submission Date: 17.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18070

18069 Xicheng Zhang, Guohuan Zhao PDF

Singular Brownian Diffusion Processes

Project: B1, B2

Published: Communications in Mathematics and Statistics 6, no. 4 (2018), 533–581

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Singular Brownian Diffusion Processes


Authors: Xicheng Zhang, Guohuan Zhao Projects: B1, B2
Submission Date: 17.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18069
Published: Communications in Mathematics and Statistics 6, no. 4 (2018), 533–581

18061 Jonas Lieber, Nadia Oudjane, Francesco Russo PDF

On the well-posedness of a class of McKean Feynman-Kac equations

Project: B1, B2

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On the well-posedness of a class of McKean Feynman-Kac equations


Authors: Jonas Lieber, Nadia Oudjane, Francesco Russo Projects: B1, B2
Submission Date: 11.12.2018 Submitter: Michael Röckner
Download: PDF Link: 18061

18048 Michael Röckner, Rongchan Zhu, Huanyu Yang PDF

Conservative stochastic 2-dimensional Cahn-Hilliard equation

Project: B1, B2

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Conservative stochastic 2-dimensional Cahn-Hilliard equation


Authors: Michael Röckner, Rongchan Zhu, Huanyu Yang Projects: B1, B2
Submission Date: 01.10.2018 Submitter: Friedrich Götze
Download: PDF Link: 18048

18045 Ting Ma, Rongchan Zhu PDF

Wong-Zakai Approximation and Support Theorem for SPDEs with Locally Monotone Coefficients

Project: B2

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Wong-Zakai Approximation and Support Theorem for SPDEs with Locally Monotone Coefficients


Authors: Ting Ma, Rongchan Zhu Projects: B2
Submission Date: 19.09.2018 Submitter: Michael Röckner
Download: PDF Link: 18045

18044 Siyu Liang, Rongchan Zhu, Ping Zhang PDF

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Project: B2

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Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity


Authors: Siyu Liang, Rongchan Zhu, Ping Zhang Projects: B2
Submission Date: 19.09.2018 Submitter: Michael Röckner
Download: PDF Link: 18044

18036 Longjie Xie, Xicheng Zhang PDF

Ergodicity of stochastic differential equations with jumps and singular coefficients

Project: B1, B2

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Ergodicity of stochastic differential equations with jumps and singular coefficients


Authors: Longjie Xie, Xicheng Zhang Projects: B1, B2
Submission Date: 24.07.2018 Submitter: Moritz Kaßmann
Download: PDF Link: 18036

18035 Xicheng Zhang, Guohuan Zhao PDF

Heat kernel and ergodicity of SDEs with distributional drifts

Project: B1, B2

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Heat kernel and ergodicity of SDEs with distributional drifts


Authors: Xicheng Zhang, Guohuan Zhao Projects: B1, B2
Submission Date: 24.07.2018 Submitter: Moritz Kaßmann
Download: PDF Link: 18035

18022 Michael Röckner, Rongchan Zhu, Xiangchan Zhu PDF

A remark on global solutions to random 3D vorticity equations for small initial data

Project: B1, B2

To appear: DCDS-B (2018)

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A remark on global solutions to random 3D vorticity equations for small initial data


Authors: Michael Röckner, Rongchan Zhu, Xiangchan Zhu Projects: B1, B2
Submission Date: 25.06.2018 Submitter: Barbara Gentz
Download: PDF Link: 18022
To appear: DCDS-B (2018)



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