Journal
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
Volume 15, Issue 1, Pages 15-35Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219891618500029
Keywords
Liquid crystal; inviscid Qian-Sheng model; dissipative solution; weak-strong uniqueness
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Funding
- European Research Council under the European Union's Seventh Framework Programme/ERC [320078]
- RVO [67985840]
- Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI [PN-II-RU-TE-2014-4-0657]
- Basque Government through the BERC program
- Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa accreditation [SEV-2013-0323]
- EntroPhase [256872]
- project Fondazione CariploRegione Lombardia MEGAsTAR Matematica d'Eccellenza in biologia ed ingegneria come acceleratore di una nuova strateGia per l'ATtRattivit a dell'ateneo pavese
- GNAMPA
- Gruppo Nazionale per l'Analisi Matematica, la Probabilit a e le loro Applicazioni of INdAM
- IMATI - C.N.R. Pavia
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We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for which a global-in-time existence theorem is shown. The dissipative solutions enjoy the following properties: (i) they exist globally in time for any finite energy initial data; (ii) dissipative solutions enjoying certain smoothness are classical solutions; (iii) a dissipative solution coincides with a strong solution originating from the same initial data as long as the latter exists.
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