Abstract
Abstract In this paper we prove some blow-up criteria for two 3D density-dependent nematic liquid crystal models in a bounded domain. MSC:35Q30, 76D03, 76D09.
Highlights
Let ⊆ R be a bounded domain with smooth boundary ∂, and let ν be the unit outward normal vector on ∂
The symbol ∇d ∇d denotes a matrix whose (i, j)th entry is ∂id ∂jd, and it is easy to find that ∇d ∇d = ∇dT ∇d
It is easy to prove that the problem ( . )-( . ) has a unique local-in-time strong solution [, ], and we omit the details here
Summary
Let ⊆ R be a bounded domain with smooth boundary ∂ , and let ν be the unit outward normal vector on ∂. It is easy to prove that the problem ) has a unique local-in-time strong solution [ , ], and we omit the details here. The aim of this paper is to consider the regularity criterion; we will prove the following theorem. Let ρ ∈ W ,q( ), u ∈ H ( ) ∩ H ( ), d ∈ H ( ) with < q ≤ and ρ ≥ , div u = in and ∂νd = on ∂ .
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