On a hyperbolic system arising in liquid crystals modeling

0488850 - MÚ 2019 RIV US eng J - Journal Article
Feireisl, Eduard - Rocca, E. - Schimperna, G. - Zarnescu, A.
On a hyperbolic system arising in liquid crystals modeling.
Journal of Hyperbolic Differential Equations. Roč. 15, č. 1 (2018), s. 15-35. ISSN 0219-8916. E-ISSN 1793-6993
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : dissipative solution * liquid crystal * weak-strong uniqueness
OECD category: Pure mathematics
Impact factor: 0.426, year: 2018
https://www.worldscientific.com/doi/abs/10.1142/S0219891618500029

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.
Permanent Link: http://hdl.handle.net/11104/0283372