Global stability and non-vanishing vacuum states for compressible nematic liquid crystal flows

We study the global stability and non-vanishing vacuum of strong solutions to the compressible nematic liquid crystal flows on the torus T3. Suppose that the density rho is bounded uniformly in Land the L-t(2) L-x(infinity)- norm of gradient of the orientation field d is bounded, we prove that the strong solution converges to an equilibrium state exponentially in L-2. This improves the previous result obtained by Chen et al. (2020) [3] where the authors require that rho(x,t) is bounded uniformly in the Holder space C-alpha for some 0 < alpha < 1 and the (Lt Lx infinity)-L-infinity-norm of gradient of d(x, t) is bounded. Moreover, our result allows the presence of vacuum. Furthermore, if additional the initial data satisfies higher regularities and the initial density possesses uniform positive lower bound, we show that the solution will converge to its equilibrium state exponentially in C-k(k E N), which provides the exponential decay rates of higher-order spatial derivatives of the solution. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.