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1.
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
2.
Global classical solution to the 3D isentropic compressible Navier–Stokes equations with general initial data and a density‐dependent viscosity coefficient
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Peixin Zhang 《Mathematical Methods in the Applied Sciences》2015,38(6):1158-1177
In this paper, we study the global existence of classical solutions to the three‐dimensional compressible Navier–Stokes equations with a density‐dependent viscosity coefficient (λ = λ(ρ)). For the general initial data, which could be either vacuum or non‐vacuum, we prove the global existence of classical solutions, under the assumption that the viscosity coefficient μ is large enough. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
3.
Yong Zhou 《Mathematical Methods in the Applied Sciences》2007,30(10):1223-1229
In this paper we derive a decay rate of the L2‐norm of the solution to the 3‐D Navier–Stokes equations. Although the result which is proved by Fourier splitting method is well known, our method is new, concise and direct. Moreover, it turns out that the new method established here has a wide application on other equations. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
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
5.
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
6.
We prove the existence of a weak solution to Navier–Stokes equations describing the isentropic flow of a gas in a convex and bounded region, ΩR2, with nonhomogeneous Dirichlet boundary conditions on ∂Ω. These results are also extended to flow domain surrounding an obstacle. 相似文献
7.
In this paper, we study the existence and regularity of solutions to the Stokes and Oseen equations with nonhomogeneous Dirichlet boundary conditions with low regularity. We consider boundary conditions for which the normal component is not equal to zero. We rewrite the Stokes and the Oseen equations in the form of a system of two equations. The first one is an evolution equation satisfied by Pu, the projection of the solution on the Stokes space – the space of divergence free vector fields with a normal trace equal to zero – and the second one is a quasi-stationary elliptic equation satisfied by (I−P)u, the projection of the solution on the orthogonal complement of the Stokes space. We establish optimal regularity results for Pu and (I−P)u. We also study the existence of weak solutions to the three-dimensional instationary Navier–Stokes equations for more regular data, but without any smallness assumption on the initial and boundary conditions. 相似文献
8.
Ben‐yu Guo 《Mathematical Methods in the Applied Sciences》2008,31(5):607-626
In this paper, we consider incompressible viscous fluid flows with slip boundary conditions. We first prove the existence of solutions of the unsteady Navier–Stokes equations in n‐spacial dimensions. Then, we investigate the stability, uniqueness and regularity of solutions in two and three spacial dimensions. In the compactness argument, we construct a special basis fulfilling the incompressibility exactly, which leads to an efficient and convergent spectral method. In particular, we avoid the main difficulty for ensuring the incompressibility of numerical solutions, which occurs in other numerical algorithms. We also derive the vorticity‐stream function form with exact boundary conditions, and establish some results on the existence, stability and uniqueness of its solutions. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
9.
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
10.
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
11.
P. Braz e Silva M. A. Rojas‐Medar E. J. Villamizar‐Roa 《Mathematical Methods in the Applied Sciences》2010,33(3):358-372
We show the existence of strong solutions for the nonhomogeneous Navier–Stokes equations in three‐dimensional domains with boundary uniformly of class C3. Under suitable assumptions, uniqueness is also proved. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
Shijin Ding Yinghua Li Ying Tang 《Mathematical Methods in the Applied Sciences》2019,42(14):4780-4794
This paper is concerned with a diffuse interface model for two‐phase flow of compressible fluids with a type of free boundary. We establish the existence and uniqueness of global strong solutions of a coupled Navier‐Stokes/Allen‐Cahn system in 1D. 相似文献
13.
In this paper, we consider the one‐dimensional compressible isentropic Navier–Stokes equations with a general ‘pressure law’ and the density‐dependent viscosity coefficient when the density connects to vacuum continuously. Precisely, the viscosity coefficient µ is proportional to ρθ and 0<θ<1, where ρ is the density. And the pressure P = P(ρ) is a general ‘pressure law’. The global existence and the uniqueness of weak solutions is proved, and a decay result for the pressure as t→ + ∞ is given. It is also proved that no vacuum states and no concentration states develop, and the free boundary do not expand to infinite. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
14.
《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
15.
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
16.
Piotr Bogusaw Mucha 《Mathematical Methods in the Applied Sciences》2001,24(9):607-622
The compressible barotropic Navier–Stokes system in monodimensional case with a Neumann boundary condition given on a free boundary is considered. The global existence with uniformly boundedness for large initial data and a positive force is proved. The result concerning an asymptotic behavior shows that the solutions tends to the stationary solution. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
17.
Vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier–Stokes equations with a slip boundary condition
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Pengfei Chen Yuelong Xiao Hui Zhang 《Mathematical Methods in the Applied Sciences》2017,40(16):5925-5932
In this paper, we investigate the vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier–Stokes equations with a slip boundary condition. We establish the local well‐posedness of the strong solutions for initial boundary value problems for such systems. Furthermore, the vanishing viscosity limit process is established, and a strong rate of convergence is obtained as the boundary of the domain is flat. In addition, it is needed to add some additional condition for density to match well the boundary condition. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
18.
Global weak solutions to the Cauchy problem of compressible Navier–Stokes–Vlasov–Fokker–Planck equations
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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
19.
Renjun Duan Tong Yang Changjiang Zhu 《Mathematical Methods in the Applied Sciences》2007,30(3):347-374
The global existence of weak solutions to the compressible Navier–Stokes equations with vacuum attracts many research interests nowadays. For the isentropic gas, the viscosity coefficient depends on density function from physical point of view. When the density function connects to vacuum continuously, the vacuum degeneracy gives some analytic difficulties in proving global existence. In this paper, we consider this case with gravitational force and fixed boundary condition. By giving a series of a priori estimates on the solution coping with the degeneracy of vacuum, gravitational force and boundary effect, we give global existence and uniqueness results similar to the case without force and boundary. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
20.
Luigi C. Berselli 《Mathematical Methods in the Applied Sciences》1999,22(13):1079-1085
In this paper we find sufficient conditions, involving only the pressure, that ensure the regularity of weak solutions to the Navier–Stokes equations. Conditions involving only the pressure were previously obtained in [7,4]. Following a remark in this last reference we improve, in particular, Kaniel's result [7]. Our condition can be seen at the light of the heuristic idea that the pressure behaves similarly to the modulus squared of the velocity. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献