Local existence of strong solutions and weak-strong uniqueness for the compressible Navier-Stokes system on moving domains

0532706 - MÚ 2021 RIV GB eng J - Journal Article
Kreml, Ondřej - Nečasová, Šárka - Piasecki, T.
Local existence of strong solutions and weak-strong uniqueness for the compressible Navier-Stokes system on moving domains.
Proceedings of the Royal Society of Edinburgh. A - Mathematics. Roč. 150, č. 5 (2020), s. 2255-2300. ISSN 0308-2105. E-ISSN 1473-7124
R&D Projects: GA MŠMT(CZ) 7AMB16PL060; GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : compressible Navier-Stokes equations * local existence * strong solution * time-dependent domain * weak-strong uniqueness
OECD category: Pure mathematics
Impact factor: 1.319, year: 2020
Method of publishing: Limited access
https://doi.org/10.1017/prm.2018.165

We consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong solutions. These results are obtained using a transformation of the problem to a fixed domain and an existence theorem for Navier–Stokes like systems with lower order terms and perturbed boundary conditions. We also show the weak–strong uniqueness principle for slip boundary conditions which remained so far open question.
Permanent Link: http://hdl.handle.net/11104/0311118