Logarithmically improved blow-up criterion for the nematic liquid crystal system with zero viscosity
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| 024 | 7 | 0 | |a 10.1007/s10231-014-0417-3 |2 doi |
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| 245 | 0 | 0 | |a Logarithmically improved blow-up criterion for the nematic liquid crystal system with zero viscosity |h [Elektronische Daten] |c [Jihong Zhao, Qiao Liu, Yining Li] |
| 520 | 3 | |a In this paper, we establish a criterion for the breakdown of local in time classical solutions to the incompressible nematic liquid crystal system with zero viscosity in dimensions three. More precisely, let $$T_{*}$$ T ∗ be the maximal existence time of the local classical solution, then $$T_{*}<+\infty $$ T ∗ < + ∞ if and only if $$\begin{aligned} \int \limits _{0}^{T_{*}}\frac{\Vert \nabla u\Vert _{\dot{B}^{0}_{\infty ,\infty }}+\Vert \nabla d\Vert _{\dot{B}^{0}_{\infty ,\infty }}^{2}}{\sqrt{1+\ln (e+\Vert \nabla u\Vert _{\dot{B}^{0}_{\infty ,\infty }} +\Vert \nabla d\Vert _{\dot{B}^{0}_{\infty ,\infty }})}}\hbox {d}t=\infty . \end{aligned}$$ ∫ 0 T ∗ ‖ ∇ u ‖ B ˙ ∞ , ∞ 0 + ‖ ∇ d ‖ B ˙ ∞ , ∞ 0 2 1 + ln ( e + ‖ ∇ u ‖ B ˙ ∞ , ∞ 0 + ‖ ∇ d ‖ B ˙ ∞ , ∞ 0 ) d t = ∞ . The result can be regarded as a corresponding logarithmical blow-up criterion inHuang and Wang (Commun. Partial Differ. Equ. 37:875-884, 2012) for the nematic liquid crystal system with zero viscosity. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Nematic liquid crystal flows |2 nationallicence | |
| 690 | 7 | |a Euler equations |2 nationallicence | |
| 690 | 7 | |a Classical solution |2 nationallicence | |
| 690 | 7 | |a Blow-up |2 nationallicence | |
| 700 | 1 | |a Zhao |D Jihong |u College of Science, Northwest A&F University, 712100, Yangling, Shaanxi, China |4 aut | |
| 700 | 1 | |a Liu |D Qiao |u Department of Mathematics, Hunan Normal University, 410081, Changsha, Hunan, China |4 aut | |
| 700 | 1 | |a Li |D Yining |u College of Mechanical and Electronic Engineering, Northwest A&F University, 712100, Yangling, Shaanxi, China |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1245-1258 |x 0373-3114 |q 194:5<1245 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0417-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0417-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhao |D Jihong |u College of Science, Northwest A&F University, 712100, Yangling, Shaanxi, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Liu |D Qiao |u Department of Mathematics, Hunan Normal University, 410081, Changsha, Hunan, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Li |D Yining |u College of Mechanical and Electronic Engineering, Northwest A&F University, 712100, Yangling, Shaanxi, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1245-1258 |x 0373-3114 |q 194:5<1245 |1 2015 |2 194 |o 10231 | ||