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Project B2: Stochastic partial differential equations with singular noise


Principal Investigator(s)
Rongchan Zhu
Xiangchan Zhu
Visitor(s)
Currently no visitors.

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:

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 scholastic 3D Navier-Stokes equations

Project: B2, B7

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Non-uniqueness in law of scholastic 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

19086 Bingguang Chen, Xiangchan Zhu PDF

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

Project: B2

To appear: Acta Mathematica Sinica, English Series (2020)

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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
To appear: Acta Mathematica Sinica, English Series (2020)

19085 Xin Chen, Bo Wu, Rongchan Zhu, Xiangchan Zhu PDF

Stochastic heat equations for infinite strings with values in a manifold

Project: B2

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Stochastic heat equations for infinite strings with values in a manifold


Authors: Xin Chen, Bo Wu, Rongchan Zhu, Xiangchan Zhu Projects: B2
Submission Date: 08.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19085

19084 Wei Liu, Rongchan Zhu PDF

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

Project: B2

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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

19083 Ting Ma, Rongchan Zhu PDF

Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus

Project: B2

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Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus


Authors: Ting Ma, Rongchan Zhu Projects: B2
Submission Date: 08.10.2019 Submitter: Michael Röckner
Download: PDF Link: 19083

18071 Kai Du, Xicheng Zhang PDF

Optimal gradient estimates of heat kernels of stable-like operators

Project: B1, B2

Published: Proceedings of American Mathematics Society 147 (2019), 3559–3565

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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
Published: Proceedings of American Mathematics Society 147 (2019), 3559–3565

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, Huanyu Yang, Rongchan Zhu PDF

Conservative stochastic 2-dimensional Cahn-Hilliard equation

Project: B1, B2

To appear: Annals of Applied Probability (2020)

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Conservative stochastic 2-dimensional Cahn-Hilliard equation


Authors: Michael Röckner, Huanyu Yang, Rongchan Zhu Projects: B1, B2
Submission Date: 01.10.2018 Submitter: Friedrich Götze
Download: PDF Link: 18048
To appear: Annals of Applied Probability (2020)

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



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