This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global...This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investigate the global regularity of 12 cases in [22]and some other new partial viscosity cases. The global regularity is established by providing new regular conditions. Our work improves some results in [22] in this sense of weaker regular criteria.展开更多
In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions ...In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.展开更多
The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transf...The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.展开更多
In this paper,we consider an initial-boundary value problem for the 2D incompressible magnetomicropolar fluid equations with zero magnetic diffusion and zero spin viscosity in the horizontally infinite flat layer with...In this paper,we consider an initial-boundary value problem for the 2D incompressible magnetomicropolar fluid equations with zero magnetic diffusion and zero spin viscosity in the horizontally infinite flat layer with Navier-type boundary conditions.We establish the global well-posedness of strong solutions around the equilibrium(0,e1,0).展开更多
In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Fur...In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Furthermore,with aid of the Fourier splitting methods,optimal time-decay rates of global smooth large solutions are also established.展开更多
基金Lin was supported by the Sichuan Science and Technology Program (2023NSFSC0056)the NNSF of China (11701049)the China Postdoctoral Science Foundation (2017M622989)。
文摘This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investigate the global regularity of 12 cases in [22]and some other new partial viscosity cases. The global regularity is established by providing new regular conditions. Our work improves some results in [22] in this sense of weaker regular criteria.
基金partially supported by the National Natural Science Foun-dation of China (10771052)Program for Science & Technology Innovation Talents in Universities of Henan Province (2009HASTIT007)+1 种基金Doctor Fund of Henan Polytechnic University (B2008-62)Innovation Scientists and Technicians Troop Construction Projects of Henan Province
文摘In this article, we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R3. We obtain the classical blow-up criteria for smooth solutions （u,w, b）, i.e., u ∈ Lq（0, T; LP（R3） for 2/q＋3/P≤ 1with 3〈P≤∞,u∈C（[0,T）;L3（R3））or△u∈Lq（0,T,LP）for 3/2〈P≤∞ satisfying 2/q＋3/P≤ 2. Moreover, our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid. In the end-point case p = ∞, the blow-up criteriacan be extended to more general spaces △u E L1 （0, T; B0∞,∞（R3）.
文摘The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman （L-S theory） and Green and Lindsay （G-L theory）. Some particular interesting cases are also deduced from the present investigation.
基金supported by National Natural Science Foundation of China(Grant No.11701049)the China Postdoctoral Science Foundation(Grant No.2017M622989)+1 种基金the Opening Fund of Geomathematics Key Laboratory of Sichuan Province(Grant No.scsxdz201707)supported by National Natural Science Foundation of China(Grant Nos.11571063 and 11771045)。
文摘In this paper,we consider an initial-boundary value problem for the 2D incompressible magnetomicropolar fluid equations with zero magnetic diffusion and zero spin viscosity in the horizontally infinite flat layer with Navier-type boundary conditions.We establish the global well-posedness of strong solutions around the equilibrium(0,e1,0).
基金supported in part by the NNSF of China(Grant No.11871212)the Basic Research Project of Key Scientific Research Project Plan of Universities in Henan Province(Grant No.20ZX002).
文摘In this paper,we investigate the initial value problem for the two-dimensiona magneto-micropolar fluid equations with partial viscosity.We prove that global existence of smooth large solutions by the energy method.Furthermore,with aid of the Fourier splitting methods,optimal time-decay rates of global smooth large solutions are also established.
基金Supported by the National Natural Science Foundation of China(10502041)The Scientific Research Foundation of Henan University of Science&Technology(0504021+1 种基金2006QN017)The Sustentation Fund Youth Skeleton Teacher in University of Henan Province
