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Blow Up Criterion for Nematic Liquid Crystal Flows [PDF]

Communications in Partial Differential Equations, 2012
In this paper, we establish a blow up criterion for the short time classical solution of the nematic liquid crystal ow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three.
Changyou Wang
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Blow-Up Criterion for Compressible MHD Equations

Journal of Mathematical Analysis and Applications, 2011
The authors study the 3D compressible magnetohydrodynamic equations. One obtains a blow up criterion for the local strong solutions just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion [\textit{J. T. Beal, T. Kato} and \textit{A. Majda}, Commun. Math. Phys.
Yi Du
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A Blow-Up Criterion of Strong Solutions to the Quantum Hydrodynamic Model

Acta Mathematica Scientia, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Guangwu, Guo, Boling
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A Blow-up Criterion for the Modified Navier–Stokes–Fourier Equations

Journal of Mathematical Fluid Mechanics, 2020
The authors study a blow-up criterion for an initial boundary value problem for the three-dimensional modified compressible Navier-Stokes-Fourier (NSF) equations proposed by \textit{H. Brenner} [``Kinematics of volume transport'', Physica A 349, No. 1--2, 11--59 (2005; \url{doi:10.1016/j.physa.2004.10.033}); ``Navier-Stokes revisited'', ibid.
Jishan Fan, Tohru Ozawa
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A Blow-Up Criterion for 3D Compressible Magnetohydrodynamic Equations With Vacuum

Mathematical Models and Methods in Applied Sciences, 2012
This paper is concerned with a blow-up criterion of strong solutions for three-dimensional compressible isentropic magnetohydrodynamic equations with vacuum. It is shown that if the density and velocity satisfy [Formula: see text], where [Formula: see text], 3 < r ≤ ∞ and [Formula: see text] denotes the weak Lr-space, then the strong solutions to ...
Xinying Xu, Jianwen Zhang
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A Blow-Up Criterion for 3D Non-Resistive Compressible Magnetohydrodynamic Equations With Initial Vacuum

Nonlinear Analysis: Real World Applications, 2011
NSFC [10801111, 10971171]; Fundamental Research Funds for the Central Universities [2010121006]; Natural Science Foundation of Fujian Province of China [2010J05011]In this paper, we prove a blow-up criterion of strong solutions to the 3D viscous and non ...
Xinying Xu, Jianwen Zhang
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Blow-Up Criterion for 3D Viscous-Resistive Compressible Magnetohydrodynamic Equations

Mathematical Methods in the Applied Sciences, 2013
In this paper, we establish a blow-up criterion of strong solutions for 3D viscous-resistive compressible magnetohydrodynamic equations, which depends only on vertical bar delta u vertical bar L1(0,T;L) and vertical bar vertical bar L(0,T;L).
Liu Shengquan
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On the blow‐up criterion of the periodic incompressible fluids

Mathematical Methods in the Applied Sciences, 2012
Kato, Ponce, Beale and Majda prove the existence and uniqueness of maximal solution of Euler and Navier–Stokes equations and some blow‐up criterion. In the periodic case, we establish that if the maximum time T* is finite, then the growth of is at least of the order of (T* − t)−2m / 5. Copyright © 2012 John Wiley & Sons, Ltd.
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A blow-up criterion for compressible nematic liquid crystal flows

Applied Mathematics and Computation, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiyi Zhu, Xiaochun Chen, Jishan Fan
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A blow-up criterion of the ideal density-dependent flows

Journal of Mathematical Analysis and Applications, 2021
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Fan, Jishan, Zhou, Yong
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