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Li, Huanyuan; Liu, Jieqiong

A blow-up criterion for the strong solutions to the two-dimensional non-isothermal inhomogeneous liquid crystal flow with density-dependent viscosity. (English) Zbl 07922068

Discrete Contin. Dyn. Syst., Ser. B 29, No. 12, 4727-4747 (2024).
Summary: We study an initial and boundary value problem to the two dimensional non-isothermal inhomogeneous nematic liquid crystal flow with non-negative density. It is shown that the strong solution exists globally if the gradient of viscosity satisfies \(\| \nabla\mu (\rho) \|_{L^{\infty} (0, T; L^p)} < \infty\). As an application, we establish the global well-posedness of strong solution to the two-dimensional non-isothermal inhomogeneous nematic liquid crystal flow with constant viscosity for general large initial data.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids

Keywords:

non-isothermal inhomogeneous liquid crystal flow; blow-up criterion; vacuum; strong solution; large initial data
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References:

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