Strong solutions to Cauchy problem of 2D compressible nematic liquid crystal flows. (English) Zbl 1366.76096
Summary: This paper studies the local existence of strong solutions to the Cauchy problem of the 2D simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows, coupled via \(\rho\) (the density of the fluid), \(u\) (the velocity of the field), and \(d\) (the macroscopic/continuum molecular orientations). Notice that the technique used for the corresponding 3D local well-posedness of strong solutions fails treating the 2D case, because the \(L^p\)-norm (\(p>2\)) of the velocity \(u\) cannot be controlled in terms only of \(\rho^{\frac{1}{2}}u\) and \(\nabla u\) here. In the present paper, under the framework of weighted approximation estimates introduced in [J. Li and Z. Liang, J. Math. Pures Appl. (9) 102, No. 4, 640–671 (2014; Zbl 1317.35177)] for Navier-Stokes equations, we obtain the local existence of strong solutions to the 2D compressible nematic liquid crystal flows.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 35B45 | A priori estimates in context of PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
Citations:
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