Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.11206 |
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Sommario:
- 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 $Q_0$.