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111.
We present some applications of a lemma by Ladyzhenskaya and Solonnikov [Determination of solutions of boundary value problems for stationary Stokes and Navier–Stokes equations having an unbounded Dirichlet integral, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980) 117–160 (English Transl.: J. Soviet Math. 21 (1983) 728–761)]. Some other results in that paper referring to stationary Navier–Stokes equations are extended to a non-Newtonian fluid, the so-called micropolar fluid. This model depends on the microrotational viscosity νr which vanishes for a Navier–Stokes fluid. We use the lemma in full to show that, as νr tends to zero, the solutions of the Ladyzhenskaya–Solonnikov problem converge to the solutions of the corresponding problem for Navier–Stokes equations. In addition, we obtain a similar convergence regarding the Leray problem for micropolar fluids. 相似文献
112.
Josipa-Pina Milišić 《Journal of Differential Equations》2018,264(9):5629-5658
In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on the saturation. Following the approach given in [13] the existence of a weak solution is proved using Galerkin approximation and regularization techniques. A priori estimates needed for passing to the limit when the regularization parameter goes to zero are obtained by using appropriate test-functions, motivated by the fact that considered PDE allows a natural generalization of the classical Kullback entropy. Finally, a special care was given in obtaining an estimate of the mixed-derivative term by combining the information from the capillary pressure with the obtained a priori estimates on the saturation. 相似文献
113.
《Mathematische Nachrichten》2018,291(14-15):2188-2203
We consider Navier–Stokes equations for compressible viscous fluids in the one‐dimensional case. We prove the existence of global strong solution with large initial data for compressible Navier–Stokes equation with viscosity coefficients of the form with (it includes in particular the important physical case of the viscous shallow water system when ). The key ingredient of the proof relies to a new formulation of the compressible equations involving a new effective velocity v (see 13 , 14 , 16 , 17 ) such that the density verifies a parabolic equation. We estimate v in norm which enables us to control the norm of by using the maximum principle. 相似文献
114.
We study the initial-boundary value problem for the one dimensional EulerBoltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified Glimm scheme to construct the global approximate solutions(U_(△t,d), I_(△t,d)) and prove that there is a subsequence of the approximate solutions which is convergent to the global solution. 相似文献
115.
Zhipeng ZHANG 《数学物理学报(B辑英文版)》2018,38(6):1655-1677
In this paper, we establish the existence of the global weak solutions for the nonhomogeneous incompressible magnetohydrodynamic equations with Navier boundary conditions for the velocity field and the magnetic field in a bounded domain ? ? R3. Furthermore,we prove that as the viscosity and resistivity coefficients go to zero simultaneously, these weak solutions converge to the strong one of the ideal nonhomogeneous incompressible magnetohydrodynamic equations in energy space. 相似文献
116.
Haibo Cui Haiyan Yin Jinshun Zhang Changjiang Zhu 《Journal of Differential Equations》2018,264(7):4564-4602
In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. . Our proof is based on the classical energy method. 相似文献
117.
We study the existence and uniqueness of a solution to a linear stationary convection–diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of two semi-infinite cylinders with two different periodic regimes. Depending on the direction of the effective convection in the two semi-infinite cylinders, we either get a unique solution, or one-parameter family of solutions, or even non-existence in the general case. In the latter case we provide necessary and sufficient conditions for the existence of a solution. 相似文献
118.
Zuoshunhua Shi 《Journal of Differential Equations》2018,264(3):1550-1580
In this paper, we mainly study the existence of self-similar solutions of stationary Navier–Stokes equations for dimension . For , if the external force is axisymmetric, scaling invariant, continuous away from the origin and small enough on the sphere , we shall prove that there exists a family of axisymmetric self-similar solutions which can be arbitrarily large in the class . Moreover, for axisymmetric external forces without swirl, corresponding to this family, the momentum flux of the flow along the symmetry axis can take any real number. However, there are no regular () axisymmetric self-similar solutions provided that the external force is a large multiple of some scaling invariant axisymmetric F which cannot be driven by a potential. In the case of dimension 4, there always exists at least one self-similar solution to the stationary Navier–Stokes equations with any scaling invariant external force in . 相似文献
119.
This paper is concerned with the global existence and large time behavior of solutions to Cauchy problem for a P1-approximation radiation hydrodynamics model. The global-in-time existence result is established in the small perturbation framework around a stable radiative equilibrium states in Sobolev space . Moreover, when the initial perturbation is also bounded in , the -decay rates of the solution and its derivatives are achieved accordingly. The proofs are based on the Littlewood–Paley decomposition techniques and elaborate energy estimates in different frequency regimes. 相似文献
120.
The problem of forced convection in a channel filled with a nanofluidsaturated porous medium is investigated, numerically. A finite difference Computational Fluid Dynamics (CFD) model with structured uniform grid system is employed to solve the momentum and energy equations. In modeling flow in the channel, the effects of flow inertia, variable porosity and Brinkman friction are taken into account. Studies are carried out for different nanoparticles with different volume fractions in the range 0%-4% and different nanoparticle diameters. Comparison made between our numerical and semi analytical Differential Transform Method (DTM) results with those in previous published research is found to be appropriate. Results show that increasing either nanoparticls volume fraction or pressure gradient parameter improves heat transfer. Further, for large quantities of nanoparticle concentration and pressure gradient, the channeling phenomenon is intensified. 相似文献