Global Regularity to the liquid crystal flows of Q-tensor model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916740003266560 |
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| author | Chen, Z. Terraneo, E. |
| author_facet | Chen, Z. Terraneo, E. |
| contents | In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when the initial data are sufficiently small, improving a result in Xiao's paper [J. Differ. Equations 2017]. The key tool of the proof is a {maximum principle.} Then, we establish also a result of continuous dependence of solutions on the
initial data. Finally, if $U=\R^3,$ based on a result of Du, Hu and Wang [Arch. Rational Mech. Anal. 2020], we give an interesting regularity criterium just via the $\dot{B}^{-1}_{\infty,\infty}$ norm of $u$ and the $L^\infty$ norm of the initial data $Q_0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Regularity to the liquid crystal flows of Q-tensor model Chen, Z. Terraneo, E. Analysis of PDEs In this paper we investigate a forced incompressible Navier-Stokes equation coupled with a parabolic type equation of Q-tensors in a domain $U\subset\R^3.$ In the case $U$ is bounded, we prove the existence of a global strong solution when the initial data are sufficiently small, improving a result in Xiao's paper [J. Differ. Equations 2017]. The key tool of the proof is a {maximum principle.} Then, we establish also a result of continuous dependence of solutions on the initial data. Finally, if $U=\R^3,$ based on a result of Du, Hu and Wang [Arch. Rational Mech. Anal. 2020], we give an interesting regularity criterium just via the $\dot{B}^{-1}_{\infty,\infty}$ norm of $u$ and the $L^\infty$ norm of the initial data $Q_0$. |
| title | Global Regularity to the liquid crystal flows of Q-tensor model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.11206 |