Mathematical analysis of fluid flows: the challenge of randomness

Project Information

FluFloRan

Grant agreement ID: 949981

DOI

10.3030/949981

Project closed

EC signature date 21 August 2020

Start date 1 March 2021

End date 28 February 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 500 000,00

EU contribution

€ 1 500 000,00

Coordinated by

UNIVERSITAET BIELEFELD
Germany

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (30)

Decay of correlations in stochastic quantization: the exponential Euclidean field in two dimensions

Author(s): Massimiliano Gubinelli, Martina Hofmanová, Nimit Rana
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, 2024, ISSN 2194-0401
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40072-024-00328-x

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

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Journal of the European Mathematical Society, Issue 1360, 2023, ISSN 1435-9863
Publisher: EMS Press
DOI: 10.4171/jems/1360

Can probability theory really help tame problems in mathematical hydrodynamics?

Author(s): Martina Hofmanová, Florian Bechtold
Published in: Mitteilungen der Deutschen Mathematiker-Vereinigung, Issue Band 30 Heft 4, 2022, ISSN 0947-4471
Publisher: Verlag de Gruyter
DOI: 10.1515/dmvm-2022-0077

Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise

Author(s): Martina Hofmanová, Theresa Lange, Umberto Pappalettera
Published in: Probability Theory and Related Fields, Issue 188, 2024, Page(s) 1183-1255, ISSN 0178-8051
Publisher: Springer Verlag
DOI: 10.1007/s00440-023-01233-5

Non-linear Young equations in the plane and pathwise regularization by noise for the stochastic wave equation

Author(s): Florian Bechtold; Fabian A. Harang; Nimit Rana
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue Volume 11, 2023, ISSN 2194-0401
Publisher: Springer Verlag
DOI: 10.1007/s40072-023-00295-9

Regularization by Noise of an Averaged Version of the Navier–Stokes Equations

Author(s): Theresa Lange
Published in: Journal of Dynamics and Differential Equations, Issue Volume 35, Issue 3, 2023, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-023-10255-5

Kolmogorov 4/5 law for the forced 3D Navier–Stokes equations

Author(s): Martina Hofmanová, Umberto Pappalettera, Rongchan Zhu, Xiangchan Zhu
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 13, 2025, Page(s) 2085-2108, ISSN 2194-0401
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40072-025-00380-1

Compressible Navier--Stokes System with Transport Noise

Author(s): Dominic Breit; Eduard Feireisl; Martina Hofmanová; Ewelina Zatorska
Published in: SIAM Journal on Mathematical Analysis, Issue 00361410, 2022, Page(s) 4465-4494, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/21m1464701

On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise

Author(s): Florian Bechtold, Theresa Lange, Jörn Wichmann
Published in: Electronic Journal of Probability, Issue 29, 2024, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/24-ejp1221

Randomness in compressible fluid flows past an obstacle

Author(s): Eduard Feireisl, Martina Hofmanova
Published in: Journal of Statistical Physics, Issue 00224715, 2022, ISSN 0022-4715
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10955-022-02879-6

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

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Annals of Probability, Issue Volume 51 (2), 2023, Page(s) 524-579, ISSN 0091-1798
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-aop1607

Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise

Author(s): Martina Hofmanová, Xiaoyutao Luo, Rongchan Zhu, Xiangchan Zhu
Published in: Mathematische Annalen, Issue 390, 2024, Page(s) 5111-5152, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-024-02881-1

Weak solutions for singular multiplicative SDEs via regularization by noise

Author(s): Florian Bechtold, Martina Hofmanová
Published in: Stochastic Processes and their Applications, Issue Volume 157, 2023, Page(s) 413-435, ISSN 0304-4149
Publisher: Elsevier BV
DOI: 10.1016/j.spa.2022.12.010

Collapse and burst of generalised surface quasi-geostrophic point vortices

Author(s): Francesco Grotto, Umberto Pappalettera
Published in: Nonlinearity, Issue 38, 2025, Page(s) 105020, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ae139a

Statistical solutions to the Schrödinger map equation in 1D, via the randomly forced Landau-Lifschitz-Gilbert equation

Author(s): Emanuela Gussetti, Martina Hofmanová
Published in: Communications in Partial Differential Equations, Issue 50, 2025, Page(s) 1291-1326, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2025.2584807

A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Journal of Functional Analysis, Issue Volume 285, Issue 5, 2023, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2023.110011

On Young regimes for locally monotone SPDEs

Author(s): Florian Bechtold, Jörn Wichmann
Published in: Journal of Differential Equations, Issue 448, 2026, Page(s) 113668, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2025.113668

Global Existence and Non-Uniqueness for 3D Navier–Stokes Equations with Space-Time White Noise

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Archive of Rational and Mechanics of Anal, Issue Nr. 247, Issue 3, Article Nr. 46, 2023, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-023-01872-x

Non-unique Ergodicity for Deterministic and Stochastic 3D Navier–Stokes and Euler Equations

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Archive for Rational Mechanics and Analysis, Issue 249, 2025, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-025-02102-2

A pathwise regularization by noise phenomenon for the evolutionary p-Laplace equation

Author(s): Florian Bechtold, Jörn Wichmann
Published in: Journal of Evolution Equations, Issue 23, 2023, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-023-00926-7

Ergodic theory for energetically open compressible fluid flows

Author(s): Francesco Fanelli, Eduard Feireisl, Martina Hofmanová
Published in: Physica D Nonlinear Phenomena, Issue Vol. 423, 132914, 2021, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2021.132914

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

Author(s): Franco Flandoli, Martina Hofmanová, Dejun Luo, Torstein Nilssen
Published in: The Annals of Applied Probability, Issue 10505164, 2022, Page(s) 2568 - 2586, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/21-aap1740

Non-uniqueness of Leray–Hopf solutions for stochastic forced Navier–Stokes equations

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Electronic Journal of Probability, Issue 29, 2024, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/24-ejp1259

On ill- and well-posedness of dissipative martingale solutions to stochastic 3D Euler equations

Author(s): Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu
Published in: Communications on Pure and Applied Mathematics, Issue 00103640, 2021, Page(s) 2446–2510, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22023

Global existence and non-uniqueness for the Cauchy problem associated to 3D Navier–Stokes equations perturbed by transport noise

Author(s): Umberto Pappalettera
Published in: Stochastics and Partial Differential Equations: Analysis and Computations, Issue 12, 2024, Page(s) 1769-1804, ISSN 2194-0401
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s40072-023-00318-5

On the 3D Navier–Stokes equations with a linear multiplicative noise and prescribed energy

Author(s): Stefanie Elisabeth Berkmeier
Published in: Journal of Evolution Equations, Issue Volume 23, Issue 3 (Article number: 43), 2023, ISSN 1424-3199
Publisher: Birkhauser Verlag
DOI: 10.1007/s00028-023-00884-0

On measure-preserving selection of solutions of ODEs

Author(s): Umberto Pappalettera
Published in: Proceedings of the American Mathematical Society, 2025, ISSN 0002-9939
Publisher: American Mathematical Society
DOI: 10.1090/proc/17097

Random dynamical system generated by the 3D Navier-Stokes equation with rough transport noise

Author(s): Jorge Cardona; Martina Hofmanová; Torstein Nilssen; Nimit Rana
Published in: Electronic Journal of Probability, Issue 10836489, 2022, ISSN 1083-6489
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ejp813

Regularization by random translation of potentials for the continuous PAM and related models in arbitrary dimension

Author(s): Bechtold, Florian
Published in: Electronic Communications in Probability, Issue Volume 27, 1-3, 2022, ISSN 1083-589X
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/22-ecp490

Anomalous and total dissipation due to advection by solutions of randomly forced Navier–Stokes equations

Author(s): Martina Hofmanová, Umberto Pappalettera, Rongcahn Zhu, Xiangchan Zhu
Published in: The Annals of Applied Probability, Issue 35, 2025, ISSN 1050-5164
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/25-aap2168