Compressible Navier-Stokes system with transport noise

Dominic Breit; Eduard Feireisl; Martina Hofmanová; Ewelina  Zatorska

doi:10.1137/21M1464701

Compressible Navier-Stokes system with transport noise

Dominic Breit, Eduard Feireisl, Martina Hofmanová, Ewelina Zatorska

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Abstract

We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both a continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the equations are understood as in the sense of the classical weak deterministic theory, (ii) the noise is rough in time and we interpret the equations in the framework of rough paths with unbounded rough drivers, and (iii) we have a Brownian noise of Stratonovich type and study the existence of martingale solutions. The first situation serves as an approximation for (ii) and (iii), while (ii) and (iii) are motivated by recent results on the incompressible Navier--Stokes system concerning the physical modeling as well as regularization by noise.

Original language	English
Pages (from-to)	4465-4494
Number of pages	30
Journal	SIAM Journal on Mathematical Analysis
Volume	54
Issue number	4
Early online date	21 Jul 2022
DOIs	https://doi.org/10.1137/21M1464701
Publication status	Published - 2022

Keywords

compressible fluids
stochastic Navier-Stokes system
transport noise

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/21M1464701

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This is the accepted version of the following article: Compressible Navier--Stokes System with Transport Noise Dominic Breit, Eduard Feireisl, Martina Hofmanová, and Ewelina Zatorska; SIAM Journal on Mathematical Analysis 2022 54:4, 4465-4494, which has been published in final form at https://doi.org/10.1137/21M1464701
Accepted author manuscript, 429 KBLicence: CC BY

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title = "Compressible Navier-Stokes system with transport noise",

abstract = "We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both a continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the equations are understood as in the sense of the classical weak deterministic theory, (ii) the noise is rough in time and we interpret the equations in the framework of rough paths with unbounded rough drivers, and (iii) we have a Brownian noise of Stratonovich type and study the existence of martingale solutions. The first situation serves as an approximation for (ii) and (iii), while (ii) and (iii) are motivated by recent results on the incompressible Navier--Stokes system concerning the physical modeling as well as regularization by noise.",

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author = "Dominic Breit and Eduard Feireisl and Martina Hofmanov{\'a} and Ewelina Zatorska",

note = "Funding Information: \ast Received by the editors December 13, 2021; accepted for publication (in revised form) April 5, 2022; published electronically July 21, 2022. https://doi.org/10.1137/21M1464701 Funding: The research of the second author leading to these results has received funding from the Czech Sciences Foundation (GACR),\v grant 21--02411S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. The third author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant 949981). The financial support by the German Science Foundation DFG via the Collaborative Research Center SFB1283 is gratefully acknowledged. The work of the fourth author was supported by the EPSRC Early Career Fellowship EP/V000586/1. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",

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N1 - Funding Information: \ast Received by the editors December 13, 2021; accepted for publication (in revised form) April 5, 2022; published electronically July 21, 2022. https://doi.org/10.1137/21M1464701 Funding: The research of the second author leading to these results has received funding from the Czech Sciences Foundation (GACR),\v grant 21--02411S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. The third author has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant 949981). The financial support by the German Science Foundation DFG via the Collaborative Research Center SFB1283 is gratefully acknowledged. The work of the fourth author was supported by the EPSRC Early Career Fellowship EP/V000586/1. Publisher Copyright: © 2022 Society for Industrial and Applied Mathematics.

PY - 2022

Y1 - 2022

N2 - We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both a continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the equations are understood as in the sense of the classical weak deterministic theory, (ii) the noise is rough in time and we interpret the equations in the framework of rough paths with unbounded rough drivers, and (iii) we have a Brownian noise of Stratonovich type and study the existence of martingale solutions. The first situation serves as an approximation for (ii) and (iii), while (ii) and (iii) are motivated by recent results on the incompressible Navier--Stokes system concerning the physical modeling as well as regularization by noise.

AB - We consider the barotropic Navier--Stokes system driven by a physically well-motivated transport noise in both a continuity as well as momentum equation. We focus on three different situations: (i) the noise is smooth in time and the equations are understood as in the sense of the classical weak deterministic theory, (ii) the noise is rough in time and we interpret the equations in the framework of rough paths with unbounded rough drivers, and (iii) we have a Brownian noise of Stratonovich type and study the existence of martingale solutions. The first situation serves as an approximation for (ii) and (iii), while (ii) and (iii) are motivated by recent results on the incompressible Navier--Stokes system concerning the physical modeling as well as regularization by noise.

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Compressible Navier-Stokes system with transport noise

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