共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we investigate the Cauchy problem for the three‐dimensional nematic liquid crystal flows with partial viscosity, and a blow up criterion of smooth solutions is established. This result is analogous to the celebrated Beale‐Kato‐Majda breakdown criterion for the incompressible Euler equations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
Dipendra Regmi 《Mathematical Methods in the Applied Sciences》2019,42(12):4305-4317
We study the global existence and regularity of classical solutions to the 2D incompressible magneto‐micropolar equations with partial dissipation. We establish the global regularity for one partial dissipation case. The proofs of our main results rely on anisotropic Sobolev type inequalities and suitable combination and cancellation of terms. 相似文献
3.
Yuming Qin Xinguang Yang Yu‐Zhu Wang Xin Liu 《Mathematical Methods in the Applied Sciences》2012,35(3):278-285
In this paper, we investigate three‐dimensional incompressible Boussinesq equations and establish some logarithmically improved blow‐up criteria of smooth solutions to the Cauchy problem for the incompressible Boussinesq equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
4.
E.E. Ortega‐Torres M.A. Rojas‐Medar R.C. Cabrales 《Numerical Methods for Partial Differential Equations》2012,28(2):689-706
We consider Galerkin approximations for the equations modeling the motion of an incompressible magneto‐micropolar fluid in a bounded domain. We derive an optimal uniform in time error bound in the H1 and L2 ‐norms for the velocity. This is done without explicit assumption of exponential stability for a class of solutions corresponding to decaying external force fields. Our study is done for no‐slip boundary conditions, but the results obtained are easily extended to the case of periodic boundary conditions. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 689–706, 2012 相似文献
5.
In this paper, we establish a blow‐up criterion of strong solutions for 3D viscous‐resistive compressible magnetohydrodynamic equations, which depends only on and . Our result improves the previous criterion in Lu's paper (Journal of Mathematical Analysis and Applications 2011; 379: 425–438.) for compressible magnetohydrodynamic equations by removing a stringent condition on the viscous coefficients μ > 4λ. In addition, initial vacuum states are also allowed in our cases. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
6.
This paper deals with radial solutions to localized reaction‐diffusion equations with variable exponents, subject to homogeneous Dirichlet boundary conditions. The global existence versus blow‐up criteria are studied in terms of the variable exponents. We proposed that the maximums of variable exponents are the key clue to determine blow‐up classifications and describe blow‐up rates for positive solutions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
Daniele Bartolucci Eugenio Montefusco 《Mathematical Methods in the Applied Sciences》2007,30(18):2309-2327
Motivated by the study of a two‐dimensional point vortex model, we analyse the following Emden–Fowler type problem with singular potential: where V(x) = K(x)/|x|2α with α∈(0, 1), 0<a?K(x)?b< + ∞, ?x∈Ω and ∥?K∥∞?C. We first extend various results, already known in case α?0, to cover the case α∈(0, 1). In particular, we study the concentration‐compactness problem and the mass quantization properties, obtaining some existence results. Then, by a special choice of K, we include the effect of the angular momentum in the system and obtain the existence of axially symmetric one peak non‐radial blow‐up solutions. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
8.
Fernando Cortez 《Mathematical Methods in the Applied Sciences》2017,40(4):1333-1345
In this paper, we consider the b‐family of equations on the torus u t ?u t x x +(b + 1)u u x =b u x u x x +u u x x x , which for appropriate values of b reduces to well‐known models, such as the Camassa–Holm equation or the Degasperis–Procesi equation. We establish a local‐in‐space blow‐up criterion. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
Blow‐up phenomena for a system of semilinear parabolic equations with nonlinear boundary conditions 下载免费PDF全文
This paper deals with the blow‐up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow‐up occurs at some finite time. We also obtain upper and lower bounds for the blow‐up time when blow‐up occurs. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Xianfa Song 《Mathematical Methods in the Applied Sciences》2007,30(10):1135-1146
In this paper, we study a system of heat equations coupled via nonlinear boundary conditions (1) Here p, q>0. We prove that the solutions always blow up in finite time for non‐trivial and non‐negative initial values. We also prove that the blow‐up occurs only on SR = ?BR for Ω = BR = {x ? ?n:|x|<R}and under some assumptions on the initial values. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
11.
Sadek Gala Yoshihiro Sawano Hitoshi Tanaka 《Mathematical Methods in the Applied Sciences》2012,35(11):1321-1334
In this work, we are interested in the study of regularity for the three‐dimensional magneto‐micropolar fluid equations in Orlicz–Morrey spaces. If the velocity field satisfies or the gradient field of velocity satisfies then we show that the solution remains smooth on [0,T]. In view of the embedding with 2 < p < 3 ∕ r and P > 1, we see that our result extends the result of Yuan and that of Gala. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
Guangwu Wang Boling Guo Shaomei Fang 《Mathematical Methods in the Applied Sciences》2017,40(14):5262-5272
In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, we study the blow‐up behaviors for the solutions of parabolic systems ut=Δu+δ1e, vt=Δv+µ1u in ?×(0, T) with nonlinear boundary conditions Here δi?0, µj?0, pi?0, qj?0 and at least one of δiµjpiqj>0(i, j=1, 2). We prove that the solutions will blow up in finite time for suitable ‘large’ initial values. The exact blow‐up rates are also obtained. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
14.
In this article, we study the blow‐up of the damped wave equation in the scale‐invariant case and in the presence of two nonlinearities. More precisely, we consider the following equation: with small initial data. For and μ ∈ (0, μ?) , where μ? > 0 is depending on the nonlinearties' powers and the space dimension (μ? satisfies ), we prove that the wave equation, in this case, behaves like the one without dissipation (μ = 0 ). Our result completes the previous studies in the case where the dissipation is given by , where, contrary to what we obtain in the present work, the effect of the damping is not significant in the dynamics. Interestingly, in our case, the influence of the damping term is important. 相似文献
15.
Huazhao Xie 《Mathematical Methods in the Applied Sciences》2011,34(2):242-248
The main purpose of this paper is concerned with blow‐up smooth solutions to Navier–Stokes–Poisson (N‐S‐P) equations. First, we present a sufficient condition on the blow up of smooth solutions to the N‐S‐P system. Then we construct a family of analytical solutions that blow up in finite time. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
16.
In this paper, we prove two results about the blow‐up criterion of the three‐dimensional incompressible Navier‐Stokes equation in the Sobolev space . The first one improves the result of Cortissoz et al. The second deals with the relationship of the blow up in and some critical spaces. Fourier analysis and standard techniques are used. 相似文献
17.
Peng Luo 《Mathematical Methods in the Applied Sciences》2015,38(12):2636-2641
By the means of a differential inequality technique, we obtain a lower bound for blow‐up time if p and the initial value satisfy some conditions. Also, we establish a blow‐up criterion and an upper bound for blow‐up time under some conditions as well as a nonblow‐up and exponential decay under some other conditions. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
18.
A. Pulkkinen 《Mathematical Methods in the Applied Sciences》2011,34(16):2011-2030
We consider the blow‐up of solutions for a semilinear reaction‐diffusion equation with exponential reaction term. It is known that certain solutions that can be continued beyond the blow‐up time possess a non‐constant self‐similar blow‐up profile. Our aim is to find the final time blow‐up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach works also for the power nonlinearity. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
The blow-up in finite time for the solutions to the initial-boundary value problem associated to the one-dimensional quantum Navier-Stokes equations in a bounded domain is proved. The model consists of the mass conservation equation and a momentum balance equation, including a nonlinear third-order differen- tial operator, with the quantum Bohm potential, and a density-dependent viscosity. It is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time, if the viscosity constant is not bigger than the scaled Planck constant. The proof is inspired by an observable constructed by Gamba, Gualdani and Zhang, which has been used to study the blowing up of solutions to quantum hydrodynamic models. 相似文献
20.
Sadek Gala Alessandra Maria Ragusa Zhuan Ye 《Mathematical Methods in the Applied Sciences》2017,40(1):279-285
Our main object is to establish a regularity criterion with p≥q > 1 for the incompressible magnetohydrodynamics equations with zero magnetic diffusivity. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献