Statistical solutions to the barotropic Navier-Stokes system

0531874 - MÚ 2021 RIV US eng J - Journal Article
Fanelli, F. - Feireisl, Eduard
Statistical solutions to the barotropic Navier-Stokes system.
Journal of Statistical Physics. Roč. 181, č. 1 (2020), s. 212-245. ISSN 0022-4715. E-ISSN 1572-9613
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : compressible Navier–Stokes system * Markov semigroup * statistical solution
OECD category: Pure mathematics
Impact factor: 1.548, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s10955-020-02577-1

We introduce a new concept of statistical solution in the framework of weak solutions to the barotropic Navier–Stokes system with inhomogeneous boundary conditions. Statistical solution is a family {Mt}t≥0 of Markov operators on the set of probability measures P[D] on the data space D containing the initial data [ϱ, m] and the boundary data dB.{Mt}t≥0 possesses a.a. semigroup property, (Formula presented.){Mt}t≥0 is deterministic when restricted to deterministic data, specifically (Formula presented.) where [ϱ, m] is a finite energy weak solution of the Navier–Stokes system corresponding to the data [ϱ, m, dB] ∈ D.Mt: P[D] → P[D] is continuous in a suitable Bregman–Wasserstein metric at measures supported by the data giving rise to regular solutions.
Permanent Link: http://hdl.handle.net/11104/0310514