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1.
Global weak solutions to the Cauchy problem of compressible Navier–Stokes–Vlasov–Fokker–Planck equations 下载免费PDF全文
Weiwei Wang 《Mathematical Methods in the Applied Sciences》2016,39(3):508-526
A fluid–particles system of the compressible Navier‐Stokes equations and Vlasov‐Fokker‐Planck equation (including the case of Vlasov equation) in three‐dimensional space is considered in this paper. The coupling arises from a drag force exerted by the fluid onto the particles. We study a Cauchy problem with large data, and establish the existence of global weak solutions through an approximation scheme, energy estimates, and weak convergence. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
2.
We study the isentropic compressible Navier–Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non‐negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ0, u 0 satisfy the compatibility condition for some radially symmetric g ∈ L2. The initial density ρ0 needs not be positive. We also prove some uniqueness results on the strong solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
In this paper, we prove the existence and uniqueness of the weak solution of the one‐dimensional compressible Navier–Stokes equations with density‐dependent viscosity µ(ρ)=ρθ with θ∈(0, γ?2], γ>1. The initial data are a perturbation of a corresponding steady solution and continuously contact with vacuum on the free boundary. The obtained results apply for the one‐dimensional Siant–Venant model of shallow water and generalize ones in (Arch. Rational Mech. Anal. 2006; 182: 223–253). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
4.
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
5.
Ewelina Zatorska 《Mathematical Methods in the Applied Sciences》2011,34(2):198-212
We study a nonlocal modification of the compressible Navier–Stokes equations in mono‐dimensional case with a boundary condition characteristic for the free boundaries problem. From the formal point of view, our system is an intermediate between the Euler and Navier–Stokes equations. Under certain assumptions, imposed on initial data and viscosity coefficient, we obtain the local and global existence of solutions. Particularly, we show the uniform in time bound on the density of fluid. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
Shijin Ding Jinrui Huang Xiao‐e Liu Huanyao Wen 《Mathematical Methods in the Applied Sciences》2011,34(12):1499-1511
In this paper, we consider the existence of global smooth solutions to 1D compressible isentropic Navier–Stokes equations with density‐dependent viscosity and free boundaries. The initial density ρ0∈W1,2n is bounded below away from zero and the initial velocity u0∈L2n. The viscosity coefficient µ is proportional to ρθ with 0<θ?1, where ρis the density. The existence and uniqueness of global solutions in Hi([0,1])(i = 1,2,4) have been established in (J. Math. Phys. 2009; 50 :023101; Meth. Appl. Anal. 2005; 12 :239–252; J. Differ. Equations 2008; 245:3956–3973; Commun. Pure Appl. Anal. 2008; 7 :373–381). By mathematical induction method, we will establish the existence of global smooth solutions to 1D compressible isentropic Navier–Stokes equations with density‐dependent viscosity and free boundaries when the initial data ρ0 and u0 are smooth. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
Koumei Tanaka 《Mathematical Methods in the Applied Sciences》2006,29(12):1451-1466
We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ?3. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula (Math. Ann. 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H3‐norm of the initial disturbance is small enough, then the solution to the non‐stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in Lq‐norm for any number q? 2. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
8.
Asymptotic stability of stationary solutions to the compressible bipolar Navier–Stokes–Poisson equations 下载免费PDF全文
In this paper, we consider the compressible bipolar Navier–Stokes–Poisson equations with a non‐flat doping profile in three‐dimensional space. The existence and uniqueness of the non‐constant stationary solutions are established when the doping profile is a small perturbation of a positive constant state. Then under the smallness assumption of the initial perturbation, we show the global existence of smooth solutions to the Cauchy problem near the stationary state. Finally, the convergence rates are obtained by combining the energy estimates for the nonlinear system and the L2‐decay estimates for the linearized equations. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
9.
We consider the Navier–Stokes equations for compressible, barotropic flow in two space dimensions, with pressure satisfying p(?)=a?logd(?) for large ?, here d>1 and a>0. After introducing useful tools from the theory of Orlicz spaces, we prove a compactness result for the solution set of the equations with respect to the variation of the underlying bounded spatial domain. Especially, we get a general existence theorem for the system in question with no restrictions on smoothness of the bounded spatial domain. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
In this paper, we study one‐dimensional compressible isentropic Navier–Stokes equations with density‐dependent viscosity. We can obtain the asymptotic stability of rarefaction waves for the compressible isentropic Navier–Stokes equations when the power of viscosity coefficient , which enlarge the range of α in the article [Jiu Q, Wang Y, Xin ZP, Communication in Partial Differential Equations 2011; 36: 602‐634]. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
Anthony Suen 《Mathematical Methods in the Applied Sciences》2014,37(17):2716-2727
We study the 3‐D compressible Navier–Stokes equations with an external potential force and a general pressure. We prove the global‐in‐time existence of weak solutions with small‐energy initial data and with densities being positive and essentially bounded. No smallness assumption is made on the external force. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
12.
Rémy Sart 《Applicable analysis》2013,92(3):357-379
This article concerns the existence of global weak solutions for a compressible Magnetohydrodynamic model. We assume the viscosity and the resistivity to be constant and we prove that Feireisl and Lions's strategies dedicated to the usual barotropic compressible flows may be extended to our system. The only difficulty to be taken into account is the magnetic field dependency. The case with density-dependent viscosity and resistivity coefficients will be treated in a forthcoming paper following Bresch and Desjardins's strategy. 相似文献
13.
Jiří Neustupa 《Mathematical Methods in the Applied Sciences》2009,32(6):653-683
We assume that Ωt is a domain in ?3, arbitrarily (but continuously) varying for 0?t?T. We impose no conditions on smoothness or shape of Ωt. We prove the global in time existence of a weak solution of the Navier–Stokes equation with Dirichlet's homogeneous or inhomogeneous boundary condition in Q[0, T) := {( x , t);0?t?T, x ∈Ωt}. The solution satisfies the energy‐type inequality and is weakly continuous in dependence of time in a certain sense. As particular examples, we consider flows around rotating bodies and around a body striking a rigid wall. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
The global weak solution of an initial-boundary value problem for a compressible non-Newtonian fluid is studied in a three-dimensional bounded domain. By the techniques of artificial pressure, a solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global weak solution to the three-dimensional compressible non-Newtonian fluid with vacuum and large data is established. 相似文献
15.
We establish the moment estimates for a class of global weak solutions to the Navier–Stokes equations in the half‐space. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
16.
We study the Navier–Stokes equations for nonhomogeneous incompressible fluids in a bounded domain Ω of R3. We first prove the existence and uniqueness of local classical solutions to the initial boundary value problem of linear Stokes equations and then we obtain the existence and uniqueness of local classical solutions to the Navier–Stokes equations with vacuum under the assumption that the data satisfies a natural compatibility condition. 相似文献
17.
Zhen Luo 《Mathematical Methods in the Applied Sciences》2014,37(9):1333-1352
In this paper, the Cauchy problem to the two‐dimensional isentropic compressible Navier–Stokes equations with smooth initial data containing vacuum is investigated. If the initial data are of small energy but possibly large oscillations, we obtain the global well‐posedness of classical solutions in the case of initially nonvacuum far fields. In particular, the smallness of the energy only depends on the norm of the initial velocity, where β can be arbitrary close to 0. In the case of compactly supported initial density, a blow‐up example is given. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
We consider the steady compressible Navier–Stokes equations of isentropic flow in three‐dimensional domains with several exits to infinity with prescribed pressure drops. On the one hand, when each exit is supposed to contain a cone inside, we shall construct bounded energy weak solution for adiabatic constant γ>3. On the other hand, when the exits do not open sufficiently rapidly, we shall prove a non‐existence result. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
19.
Masao Yamazaki 《Mathematische Nachrichten》2016,289(17-18):2281-2311
This paper is concerned with the stationary Navier–Stokes equation in the whole plane and in the two–dimensional exterior domain invariant under the action of the cyclic group of order 4, and gives a condition on the potentials yielding the external force, and on the boundary value, sufficient for the unique existence of a small solution equivariant with respect to the aforementioned cyclic group. 相似文献
20.
We prove existence, uniqueness and exponential stability of stationary Navier–Stokes flows with prescribed flux in an unbounded cylinder of ?n,n?3, with several exits to infinity provided the total flux and external force are sufficiently small. The proofs are based on analytic semigroup theory, perturbation theory and Lr ? Lq‐estimates of a perturbation of the Stokes operator in Lq‐spaces. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献