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1.
In this short paper, the initial value problem for the Navier‐Stokes equations with the Coriolis force is investigated. The Coriolis force appears in almost all of the models of meteorology and geophysics dealing with large‐scale phenomena. We prove that existence of uniform global large solutions to the Navier‐Stokes equations with the Coriolis force for a class of special initial data. The results obtained in this paper are different from the previous 2 types of results.  相似文献   

2.
We consider the Navier–Stokes equations in the rotational framework with the time periodic external force. We give sufficient conditions on the size of the external forces for the existence of time periodic solutions in terms of the Coriolis parameter. It follows from our conditions that the unique existence of time periodic solutions is guaranteed for large external forces provided the speed of rotation is sufficiently fast.  相似文献   

3.
In this article we study the asymptotic behavior of solutions of the primitive equations (PEs) as the depth of the domain goes to zero. We prove that the solutions of the PEs can be expanded as a sum of barotropic flow and baroclinic flow up to a uniformly bounded (in time and space) initial time layer. The barotropic flow is solution of the 2D Navier–Stokes equations with Coriolis force coupled with density. By employing a comparison theorem, the baroclinic flow can be approximated by a quasi-stationary nonlinear GFD-Stokes problem. This article presents a mathematically rigorous justification that the barotropic flow dominates the baroclinic flow in the motion of the atmosphere and ocean.  相似文献   

4.
In this paper, we are concerned with the system of the non‐isentropic compressible Navier–Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time‐decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large‐time behavior is based on the linearized analysis of the non‐isentropic Navier–Stokes–Poisson equations and the electromagnetic part for the linearized isentropic Navier–Stokes–Maxwell equations. In the meantime, the time‐decay rates obtained by Zhang, Li, and Zhu [J. Differential Equations, 250(2011), 866‐891] for the linearized non‐isentropic Navier–Stokes–Poisson equations are improved. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
We study the existence theory for the Cucker–Smale–Navier–Stokes (in short, CS–NS) equations in two dimensions. The CS–NS equations consist of Cucker–Smale flocking particles described by a Vlasov-type equation and incompressible Navier–Stokes equations. The interaction between the particles and fluid is governed by a drag force. In this study, we show the global existence of weak solutions for this system. We also prove the global existence and uniqueness of strong solutions. In contrast with the results of Bae et al. (2014) on the CS–NS equations considered in three dimensions, we do not require any smallness assumption on the initial data.  相似文献   

6.
In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case.  相似文献   

7.
In this paper, we consider the one-dimensional (1D) compressible bipolar Navier–Stokes–Poisson equations. We know that when the viscosity coefficient and Debye length are zero in the compressible bipolar Navier–Stokes–Poisson equations, we have the compressible Euler equations. Under the case that the compressible Euler equations have a rarefaction wave with one-side vacuum state, we can construct a sequence of the approximation solution to the one-dimensional bipolar Navier–Stokes–Poisson equations with well-prepared initial data, which converges to the above rarefaction wave with vacuum as the viscosity and the Debye length tend to zero. Moreover, we also obtain the uniform convergence rate. The results are proved by a scaling argument and elaborate energy estimate.  相似文献   

8.
This article is concerned with the asymptotical behavior of solutions for the three-dimensional damped Navier–Stokes equations with additive noise. Due to the shortage of the existence proof of the existence of random absorbing sets in a more regular phase space, we cannot obtain some kind of compactness of the cocycle associated with the three-dimensional damped Navier–Stokes equations with additive noise by the Sobolev compactness embedding theorem. In this paper, we prove the existence of a random attractor for the three-dimensional damped Navier–Stokes equations with additive noise by verifying the pullback flattening property.  相似文献   

9.
In this paper, we investigate nonhomogeneous incompressible Navier–Stokes–Landau–Lifshitz system in two-dimensional (2-D). This system consists of Navier–Stokes equations coupled with Landau–Lifshitz–Gilbert equation, an evolutionary equation for the magnetization vector. We establish a blowup criterion for the 2-D incompressible Navier–Stokes–Landau–Lifshitz system with finite positive initial density.  相似文献   

10.
The velocity–vorticity formulation of the 3D Navier–Stokes equations was recently found to give excellent numerical results for flows with strong rotation. In this work, we propose a new regularization of the 3D Navier–Stokes equations, which we call the 3D velocity–vorticity-Voigt (VVV) model, with a Voigt regularization term added to momentum equation in velocity–vorticity form, but with no regularizing term in the vorticity equation. We prove global well-posedness and regularity of this model under periodic boundary conditions. We prove convergence of the model's velocity and vorticity to their counterparts in the 3D Navier–Stokes equations as the Voigt modeling parameter tends to zero. We prove that the curl of the model's velocity converges to the model vorticity (which is solved for directly), as the Voigt modeling parameter tends to zero. Finally, we provide a criterion for finite-time blow-up of the 3D Navier–Stokes equations based on this inviscid regularization.  相似文献   

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