@article{ca2e61b8652b4bb5a7cf802ec756dbc2,
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.",
keywords = "compressible fluids, stochastic Navier-Stokes system, transport noise",
author = "Dominic Breit and Eduard Feireisl and Martina Hofmanov{\'a} and Ewelina Zatorska",
note = "Funding Information: \textbackslash{}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),\textbackslash{}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.",
year = "2022",
doi = "10.1137/21M1464701",
language = "English",
volume = "54",
pages = "4465--4494",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}