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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.
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21036
Rongchan Zhu, Xiangchan Zhu, Martina Hofmanová PDF
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 |
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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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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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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 (2021), 1846–1898 |
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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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20111
Dominic Breit, Eduard Feireisl, Martina Hofmanová PDF
On the long time behavior of compressible fluid flows excited by random forcing Project: B7 |
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20104
Martina Hofmanová, Rongchan Zhu, Xiangchan Zhu PDF
On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations Published: Communications on Pure and Applied Mathematics 75, no. 11 (2022), 2446–2510 |
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20102
Anna Balci, Mikhail Surnachev PDF
Lavrentiev gap for some classes of generalized Orlicz functions Project: B7 |
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20097
Xingang Wen, L’ubomír Baňas, Herbert Dawid, Tsiry Avisoa Randrianasolo, Johannes Storn PDF
Published: Journal of Scientific Computing 92, no. 54 (2022) Notes: DOI: 10.1007/s10915-022-01892-x
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On numerical approximation of a system of Hamilton-Jacobi-Bellman equations arising in innovation dynamics |
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20065
Dominic Breit, Lars Diening, Johannes Storn, Jörn Wichmann PDF
The parabolic p-Laplacian with fractional differentiability Project: B7 Published: IMA Journal of Numerical Analysis (2020) Notes: https://doi.org/10.1093/imanum/draa081 |
