Weak solution to compressible hydrodynamic flow of liquid crystals in dimension one
The authors consider the equation modeling the compressible hydrodynamic flow of liquid crystals in one dimension. One establishes the existence of a weak solution \((\rho,u,n)\) of such a system when the initial density function \(0\leq\rho_0\in L^\gamma\) for \(\gamma>1\), \(u_0\in L^2\) and \(n_0\in H^1\). This extends a previous result of the authors, where the existence of a weak solution was obtained under the stronger assumption that the initial density function \(0<c\leq \rho_0\in H^1\), \(u_0\in L^2\) and \(n_0\in H^1\).
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