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《Journal of the Egyptian Mathematical Society》2014,22(1):143-151
The influences of Hall current and slip condition on the MHD flow induced by sinusoidal peristaltic wavy wall in two dimensional viscous fluid through a porous medium for moderately large Reynolds number is considered on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for the outer and inner flows for various values of the Reynolds number, slip parameter, Hall and magnetic parameters are drawn. The inner and outer solutions are matched by the matching process. An interesting application of the present results to mechanical engineering may be the possibility of the fluid transportation without an external pressure. 相似文献
73.
The low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space R3. First, the uniform-in-Mach-number estimates of the solutions in a Sobolev space are established on a finite time interval independent of the Mach number. Then the low Mach number limit is proved by combining these uniform estimate with a theorem due to Métivier and Schochet (2001) [45] for the Euler equations that gives the local energy decay of the acoustic wave equations. 相似文献
74.
The Cauchy problem of the relativistic Landau–Maxwell system in R3 is investigated. For perturbative initial data with suitable regularity and integrability, we obtain the optimal large-time decay rates of the relativistic Landau–Maxwell system. For the proof, a new interactive instant energy functional is introduced to capture the macroscopic dissipation and the very weak electromagnetic dissipation of the linearized system. The iterative method is applied to handle the time-decay rates of the full instant energy functional because of the regularity-loss property of the electromagnetic field. 相似文献
75.
The partial regularity of the suitable weak solutions to the Navier–Stokes equations in Rn with n=2,3,4 and the stationary Navier–Stokes equations in Rn for n=2,3,4,5,6 are investigated in this paper. Using some elementary observation of these equations together with De Giorgi iteration method, we present a unified proof on the results of Caffarelli, Kohn and Nirenberg [1], Struwe [17], Dong and Du [5], and Dong and Strain [7]. Particularly, we obtain the partial regularity of the suitable weak solutions to the 4d non-stationary Navier–Stokes equations, which improves the previous result of [5], where Dong and Du studied the partial regularity of smooth solutions of the 4d Navier–Stokes equations at the first blow-up time. 相似文献
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The possibility of finite-time, dispersive blow-up for nonlinear equations of Schrödinger type is revisited. This mathematical phenomena is one of the conceivable explanations for oceanic and optical rogue waves. In dimension one, the fact that dispersive blow up does occur for nonlinear Schrödinger equations already appears in [9]. In the present work, the existing results are extended in several ways. In one direction, the theory is broadened to include the Davey–Stewartson and Gross–Pitaevskii equations. In another, dispersive blow up is shown to obtain for nonlinear Schrödinger equations in spatial dimensions larger than one and for more general power-law nonlinearities. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel's formula is obtained. 相似文献
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