Global strong solutions to the one-dimensional full compressible liquid crystal equations with temperature-dependent heat conductivity

Global solution to the compressible non-isothermal nematic liquid crystal equations with constant heat conductivity and vacuum

“…Thus our result improves the results of [56,57] for κ(θ ) = θ β with β = 0, which does not include the constant case.…”

“…To our best knowledge, global strong solution to one-dimensional non-isothermal compressible nematic liquid crystal equations for arbitrary large initial data is not known for constant coefficients and vacuum. The global solution obtained for system (1.5) in Mei [56], Li et al, [57] holds for β > 0 with ρ 0 ≥ C. Similarly, the result obtained in [55] with vacuum in Euler coordinates is restricted to the condition on heat conductivity of type (1.4). Motivated by Kazhikhov [35] and Li [50], in this paper we aim to study the global well-posedness of strong solutions to the one-dimensional non-isothermal compressible nematic liquid crystal flow equations, i.e., system (1.5), with constant viscosity and heat conductivity in the presence of vacuum.…”

“…The result [54] was extended by Mei [56] in 2020, where the author proved global classical solution to the free boundary value problem in the presence of temperature equation with heat conductivity of type (1.4). By using the stronger assumption on heat conductivity (1.3), recently, in 2021, Li, Mahmood, and Shang [57] obtained the global strong solution with ρ 0 ≥ C.…”

Globe strong solutions to the 1-D non-isothermal compressible liquid crystal equations accounting for stretching term

“…and inspired by Yu [29] and Liu [1], in this paper we aim to study the global strong solutions of one-dimensional non-isothermal compressible liquid crystal equations with stretching terms.We introduce a stretching term to make the liquid crystal dynamics model more general, while the energy equation still holds.Similar results are obtained for [30] and [31] when heat conductivity coefficient is a constant and κ(θ) = θ β , respectively In rest of this paper is organized as follows.In Section 1,we derive the equivalence system in Lagrangian coordinates as well as state the results.The lower and higher order a prior estimates are derived in Section 2 and Section 3 respectively.Theorem 1 is proven in the section 4.In the appendix, an one-dimensional generalized Poincare-type inequality is provided, which is commonly utilized in a priori estimates.…”