Existence and asymptotic behavior to the incompressible nematic liquid crystal flow in the whole space |
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| Authors: | Minghua Yang Jinyi Sun |
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| Affiliation: | Department of Mathematics, Sun Yat‐sen University, Guangzhou, China |
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| Abstract: | In this article, first of all, the global existence and asymptotic stability of solutions to the incompressible nematic liquid crystal flow is investigated when initial data are a small perturbation near the constant steady state (0,δ0); here, δ0 is a constant vector with |δ0|=1. Precisely, we show the existence and asymptotic stability with small initial data  for  . The initial data class  of us is not entirely included in the space BMO?1×BMO and contains strongly singular functions and measures. As an application, we obtain a class of asymptotic existence of a basin of attraction for each self‐similar solution with homogeneous initial data. We also study global existence of a large class of decaying solutions and construct an explicit asymptotic formula for ∣x∣→∞, relating the self‐similar profile (U(x),D(x)) to its corresponding initial data (u0,d0). In two dimensions, we obtain higher‐order asymptotics of (u(x),d(x)). Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | incompressible nematic liquid crystal flow self‐similarity asymptotic profiles asymptotic stability Besov– Morrey space Morrey space |
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