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Project B7.1: Stochastic non-Newtonian Fluids: Regularity and Numerics


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Summary:

We are concerned with stochastic partial differential equations appearing in the modeling of non-Newtonian fluids. More precisely, we study models such as p-Navier--Stokes system where randomness is encoded in two ways: in the form of a random initial datum and in the form of stochastic external forces given by a general (nonlinear) multiplicative noise. Within the first part, we aim at developing a regularity theory. In particular, we are interested in the natural regularity which is essential for numerical approximations. The second part of our project is concerned with developing efficient numerical schemes and proving their rates of convergence.


Recent Preprints:

21086 Lars Diening, Anna Balci, Andrea Cianchi, Vladimir Maz'ya PDF

A pointwise differential inequality and second-order regularity for nonlinear elliptic systems

Project: B7

Published: Mathematische Annalen 383 (2022), 1775–1824

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A pointwise differential inequality and second-order regularity for nonlinear elliptic systems


Authors: Lars Diening, Anna Balci, Andrea Cianchi, Vladimir Maz'ya Projects: B7
Submission Date: 11.01.2022 Submitter: Martina Hofmanová
Download: PDF Link: 21086
Published: Mathematische Annalen 383 (2022), 1775–1824

21085 Lars Diening, Johannes Storn, Tabea Tscherpel PDF

Fortin Operator for the Taylor-Hood Element

Project: B7

Published: Numerische Mathematik 150 (2022), 671–689

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Fortin Operator for the Taylor-Hood Element


Authors: Lars Diening, Johannes Storn, Tabea Tscherpel Projects: B7
Submission Date: 11.01.2022 Submitter: Martina Hofmanová
Download: PDF Link: 21085
Published: Numerische Mathematik 150 (2022), 671–689

21084 Lars Diening, Franz Gmeineder PDF

Sharp trace and Korn inequalities for differential operators

Project: B7

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Sharp trace and Korn inequalities for differential operators


Authors: Lars Diening, Franz Gmeineder Projects: B7
Submission Date: 11.01.2022 Submitter: Martina Hofmanová
Download: PDF Link: 21084

21083 Lars Diening, Mikyoung Lee, Jihoon Ok PDF

Parabolic weighted Sobolev-Poincaré type inequalities

Project: B7

Published: Nonlinear Analysis 218 (2022), Paper No. 112772, 13 pp.

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Parabolic weighted Sobolev-Poincaré type inequalities


Authors: Lars Diening, Mikyoung Lee, Jihoon Ok Projects: B7
Submission Date: 11.01.2022 Submitter: Martina Hofmanová
Download: PDF Link: 21083
Published: Nonlinear Analysis 218 (2022), Paper No. 112772, 13 pp.

21080 Dominic Breit, Martina Hofmanová, Eduard Feireisl PDF

Stationary solutions in thermodynamics of stochastically forced fluids

Project: B7

Published: Mathematische Annalen 384 (2022), 1127–1155

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Stationary solutions in thermodynamics of stochastically forced fluids


Authors: Dominic Breit, Martina Hofmanová, Eduard Feireisl Projects: B7
Submission Date: 11.01.2022 Submitter: Lars Diening
Download: PDF Link: 21080
Published: Mathematische Annalen 384 (2022), 1127–1155

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

21016 Eduard Feireisl, Martina Hofmanová PDF

Randomness in compressible fluid flows past an obstacle

Project: B7

Published: Journal of Statistical Physics 186, no. 32 (2022)

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Randomness in compressible fluid flows past an obstacle


Authors: Eduard Feireisl, Martina Hofmanová Projects: B7
Submission Date: 21.01.2021 Submitter: Lars Diening
Download: PDF Link: 21016
Published: Journal of Statistical Physics 186, no. 32 (2022)

20136 Lars Diening, Johannes Storn, Tabea Tscherpel PDF

On the Sobolev and $L^p$-Stability of the $L^2$-projection

Project: B7

To appear: SIAM Journal on Numerical Analysis (2021)

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On the Sobolev and $L^p$-Stability of the $L^2$-projection


Authors: Lars Diening, Johannes Storn, Tabea Tscherpel Projects: B7
Submission Date: 20.01.2021 Submitter: Martina Hofmanová
Download: PDF Link: 20136
To appear: SIAM Journal on Numerical Analysis (2021)

20135 Lars Diening, Toni Scharle, Endre Süli PDF

Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations

Project: B7

Published: IMA Journal of Numerical Analysis 41, no. 3 (2021), 1846–1898

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Uniform Hölder-norm bounds for finite element approximations of second-order elliptic equations


Authors: Lars Diening, Toni Scharle, Endre Süli Projects: B7
Submission Date: 20.01.2021 Submitter: Martina Hofmanová
Download: PDF Link: 20135
Published: IMA Journal of Numerical Analysis 41, no. 3 (2021), 1846–1898

20113 Lars Diening, Johannes Storn PDF

A Space-Time DPG Method for the Heat Equation

Project: B7

Published: Computers & Mathematics with Applications 105 (2022), 41−53

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A Space-Time DPG Method for the Heat Equation


Authors: Lars Diening, Johannes Storn Projects: B7
Submission Date: 26.12.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20113
Published: Computers & Mathematics with Applications 105 (2022), 41−53


All Publications of this Project


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