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Project B2.1: Stochastic partial differential equations with singular noise


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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:

21036 Rongchan Zhu, Xiangchan Zhu, Martina Hofmanová PDF

Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

Project: B1, B2, B7

Published: Ann. Probab. 51 (2023), 524–579

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Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness


Authors: Rongchan Zhu, Xiangchan Zhu, Martina Hofmanová Projects: B1, B2, B7
Submission Date: 04.05.2021 Submitter: Sebastian Herr
Download: PDF Link: 21036
Published: Ann. Probab. 51 (2023), 524–579

20126 Hao Shen, Scott Smith, Rongchan Zhu, Xiangchan Zhu PDF

Large $N$ Limit of the $O(N)$ Linear Sigma Model via Stochastic Quantization

Project: B2

Published: Ann. Probab. 50, no. 1 (2022), 131–202

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Large $N$ Limit of the $O(N)$ Linear Sigma Model via Stochastic Quantization


Authors: Hao Shen, Scott Smith, Rongchan Zhu, Xiangchan Zhu Projects: B2
Submission Date: 30.12.2020 Submitter: Benjamin Gess
Download: PDF Link: 20126
Published: Ann. Probab. 50, no. 1 (2022), 131–202

20125 Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu PDF

Singular HJB Equations with Applications to KPZ on the Real Line

Project: B1, B2

Published: Probab. Theory Relat. Fields 183, no. 3–4 (2022), 789–869

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Singular HJB Equations with Applications to KPZ on the Real Line


Authors: Xicheng Zhang, Rongchan Zhu, Xiangchan Zhu Projects: B1, B2
Submission Date: 30.12.2020 Submitter: Benjamin Gess
Download: PDF Link: 20125
Published: Probab. Theory Relat. Fields 183, no. 3–4 (2022), 789–869

20104 Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu PDF

On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations

Project: B2, B7

Published: Communications on Pure and Applied Mathematics 75, no. 11 (2022), 2446–2510

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On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations


Authors: Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu Projects: B2, B7
Submission Date: 14.10.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20104
Published: Communications on Pure and Applied Mathematics 75, no. 11 (2022), 2446–2510

20059 Bingguang Chen, Xiangchan Zhu PDF

Large deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity

Project: B2

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Large deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity


Authors: Bingguang Chen, Xiangchan Zhu Projects: B2
Submission Date: 29.05.2020 Submitter: Michael Röckner
Download: PDF Link: 20059

20006 Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu PDF

Non-uniqueness in law of stochastic 3D Navier-Stokes equations

Project: B2, B7

To appear: J. Eur. Math. Soc. (JEMS) (2023)

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Non-uniqueness in law of stochastic 3D Navier-Stokes equations


Authors: Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu Projects: B2, B7
Submission Date: 02.01.2020 Submitter: Michael Röckner
Download: PDF Link: 20006
To appear: J. Eur. Math. Soc. (JEMS) (2023)

19112 Huanyu Yang, Rongchan Zhu PDF

Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations

Project: B2

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Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations


Authors: Huanyu Yang, Rongchan Zhu Projects: B2
Submission Date: 17.01.2021 Submitter: Michael Röckner
Download: PDF Link: 19112

19111 L’ubomír Baňas, Huanyu Yang, Rongchan Zhu PDF

Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise

Project: B2, B3

Published: Potential Analysis 59 (2023), 497–51

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Sharp interface limit of stochastic Cahn-Hilliard equation with singular noise


Authors: L’ubomír Baňas, Huanyu Yang, Rongchan Zhu Projects: B2, B3
Submission Date: 17.01.2021 Submitter: Michael Röckner
Download: PDF Link: 19111
Published: Potential Analysis 59 (2023), 497–51

19086 Bingguang Chen, Xiangchan Zhu PDF

On the small time asymptotics of the dynamical $\Phi_1^4$ model

Project: B2

Published: Acta Mathematica Sinica, English Series (2020)

Notes: DOI: 10.1007/s10114-020-9342-0

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On the small time asymptotics of the dynamical $\Phi_1^4$ model


Authors: Bingguang Chen, Xiangchan Zhu Projects: B2
Submission Date: 09.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19086
Published: Acta Mathematica Sinica, English Series (2020)
Notes: DOI: 10.1007/s10114-020-9342-0

19084 Wei Liu, Rongchan Zhu PDF

Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition

Project: B2

Published: Forum of Mathematics 32, no. 3 (2020), 723–738

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Well-posedness of Backward Stochastic Partial Differential Equations with Lyapunov Condition


Authors: Wei Liu, Rongchan Zhu Projects: B2
Submission Date: 08.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19084
Published: Forum of Mathematics 32, no. 3 (2020), 723–738


All Publications of this Project


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