The solvability for a nonlinear degenerate hyperbolic-parabolic coupled system arising from nematic liquid crystals

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Heat equation (35K05) Liquid crystals (76A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Degenerate hyperbolic equations (35L80) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Classical solutions to PDEs (35A09)

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