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



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:

20104 Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu PDF

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

Project: B7

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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: B7
Submission Date: 14.10.2020 Submitter: Moritz Kaßmann
Download: PDF Link: 20104

20102 Anna Khripunova-Balci, Mikhail Surnachev PDF

Lavrentiev gap for some classes of generalized Orlicz functions

Project: B7

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Lavrentiev gap for some classes of generalized Orlicz functions


Authors: Anna Khripunova-Balci, Mikhail Surnachev Projects: B7
Submission Date: 09.10.2020 Submitter: Sebastian Herr
Download: PDF Link: 20102

20097 L’ubomír Baňas, Herbert Dawid, Tsiry Avisoa Randrianasolo, Johannes Storn, Xingang Wen PDF

On numerical approximation of a system of Hamilton-Jacobi-Bellman equations arising in innovation dynamics

Project: B3, B7, C2

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On numerical approximation of a system of Hamilton-Jacobi-Bellman equations arising in innovation dynamics


Authors: L’ubomír Baňas, Herbert Dawid, Tsiry Avisoa Randrianasolo, Johannes Storn, Xingang Wen Projects: B3, B7, C2
Submission Date: 28.08.2020 Submitter: Giorgio Ferrari
Download: PDF Link: 20097

20065 Dominic Breit, Lars Diening, Johannes Storn, Jörn Wichmann PDF

The parabolic p-Laplacian with fractional differentiability

Project: B7

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The parabolic p-Laplacian with fractional differentiability


Authors: Dominic Breit, Lars Diening, Johannes Storn, Jörn Wichmann Projects: B7
Submission Date: 29.06.2020 Submitter: Martina Hofmanová
Download: PDF Link: 20065

20061 Francesco Fanelli, Eduard Feireisl, Martina Hofmanová PDF

Ergodic theory for energetically open compressible fluid flows

Project: B7

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Ergodic theory for energetically open compressible fluid flows


Authors: Francesco Fanelli, Eduard Feireisl, Martina Hofmanová Projects: B7
Submission Date: 04.06.2020 Submitter: L’ubomír Baňas
Download: PDF Link: 20061

20050 Franco Flandoli, Martina Hofmanová, Dejun Luo, Torstein Nilssen PDF

Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field

Project: B7

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Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field


Authors: Franco Flandoli, Martina Hofmanová, Dejun Luo, Torstein Nilssen Projects: B7
Submission Date: 13.05.2020 Submitter: Sebastian Herr
Download: PDF Link: 20050

20035 Anna Khripunova-Balci, Lars Diening, Markus Weimar PDF

Higher order Calderon-Zygmund estimates for the p-Laplace equation

Project: B7

Published: Journal of Differential Equations 268 (2020), 590–635

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Higher order Calderon-Zygmund estimates for the p-Laplace equation


Authors: Anna Khripunova-Balci, Lars Diening, Markus Weimar Projects: B7
Submission Date: 06.04.2020 Submitter: Sebastian Herr
Download: PDF Link: 20035
Published: Journal of Differential Equations 268 (2020), 590–635

20034 Anna Khripunova-Balci, Lars Diening, Mikhail Surnachev PDF

New Examples on Lavrentiev Gap Using Fractals

Project: B7

Published: Calculus of Variations and Partial Differential Equations 59, no. 180 (2020)

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New Examples on Lavrentiev Gap Using Fractals


Authors: Anna Khripunova-Balci, Lars Diening, Mikhail Surnachev Projects: B7
Submission Date: 06.04.2020 Submitter: Sebastian Herr
Download: PDF Link: 20034
Published: Calculus of Variations and Partial Differential Equations 59, no. 180 (2020)

20033 Anna Khripunova-Balci, Lars Diening, Raffaella Giova, Antonia Passarelli di Napoli PDF

Elliptic Equations With Degenerate weights

Project: B7

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Elliptic Equations With Degenerate weights


Authors: Anna Khripunova-Balci, Lars Diening, Raffaella Giova, Antonia Passarelli di Napoli Projects: B7
Submission Date: 06.04.2020 Submitter: Sebastian Herr
Download: PDF Link: 20033

20032 Lars Diening, Christian Kreuzer PDF

On the threshold condition for Dörfler marking

Project: B7

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On the threshold condition for Dörfler marking


Authors: Lars Diening, Christian Kreuzer Projects: B7
Submission Date: 06.04.2020 Submitter: Sebastian Herr
Download: PDF Link: 20032



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