On well-posedness of quantum fluid systems in the class of dissipative solutions

0573353 - MÚ 2024 RIV US eng J - Journal Article
Basarić, Danica - Tang, T.
On well-posedness of quantum fluid systems in the class of dissipative solutions.
SIAM Journal on Mathematical Analysis. Roč. 55, č. 3 (2023), s. 2434-2466. ISSN 0036-1410. E-ISSN 1095-7154
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : quantum fluid systems * dissipative solutions * semiflow selection
OECD category: Pure mathematics
Impact factor: 2, year: 2022
Method of publishing: Limited access
https://doi.org/10.1137/22M148985

The main objects of the present work are the quantum Navier–Stokes and quantum Euler systems, for the first one, in particular, we will consider constant viscosity coefficients. We deal with the concept of dissipative solutions, for which we will first prove the weak-strong uniqueness principle, and afterward, we will show the global existence for any finite energy initial data. Finally, we will prove that both systems admit a semiflow selection in the class of dissipative solutions.
Permanent Link: https://hdl.handle.net/11104/0343814