共查询到20条相似文献,搜索用时 15 毫秒
1.
Existence of global weak solutions for Navier‐Stokes‐Poisson equations with quantum effect and convergence to incompressible Navier‐Stokes equations 下载免费PDF全文
In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier‐Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
2.
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
3.
《Mathematical Methods in the Applied Sciences》2018,41(4):1424-1438
In this paper, we are concerned with optimal decay rates for higher‐order spatial derivatives of classical solution to the compressible Navier‐Stokes‐Maxwell equations in three‐dimensional whole space. If the initial perturbation is small in ‐norm, we apply the Fourier splitting method to establish optimal decay rates for the second‐order spatial derivatives of a solution. As a by‐product, the rate of classical solution converging to the constant equilibrium state in ‐norm is . 相似文献
4.
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
5.
This paper is dedicated to the study of the Navier‐Stokes‐Landau‐Lifshitz system. We obtain the global existence of a unique solution for this system without any small conditions imposed on the third component of the initial velocity field. Our methods mainly rely upon the Fourier frequency localization and Bony's paraproduct decomposition. 相似文献
6.
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
7.
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
8.
Zero‐viscosity‐capillarity limit to rarefaction waves for the 1D compressible Navier–Stokes–Korteweg equations 下载免费PDF全文
In this paper, we study the zero viscosity and capillarity limit problem for the one‐dimensional compressible isentropic Navier–Stokes–Korteweg equations when the corresponding Euler equations have rarefaction wave solutions. In the case that either the effects of initial layer are ignored or the rarefaction waves are smooth, we prove that the solutions of the Navier–Stokes–Korteweg equation with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity and capillarity number vanish, and we also obtain a rate of convergence, which is valid uniformly for all time. These results are showed by a scaling argument and elementary energy analysis. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
9.
Uniform regularity and vanishing viscosity limit for the chemotaxis‐Navier‐Stokes system in a 3D bounded domain 下载免费PDF全文
Zhipeng Zhang 《Mathematical Methods in the Applied Sciences》2017,40(18):7564-7597
We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis‐Navier‐Stokes system with Navier boundary condition for velocity field and Neumann boundary condition for cell density and chemical concentration in a 3D bounded domain. It is shown that there exists a unique strong solution of the incompressible chemotaxis‐Navier‐Stokes system in a finite time interval, which is independent of the viscosity coefficient. Moreover, this solution is uniformly bounded in a conormal Sobolev space, which allows us to take the vanishing viscosity limit to obtain the incompressible chemotaxis‐Euler system. 相似文献
10.
Huazhao Xie 《Mathematical Methods in the Applied Sciences》2011,34(2):242-248
The main purpose of this paper is concerned with blow‐up smooth solutions to Navier–Stokes–Poisson (N‐S‐P) equations. First, we present a sufficient condition on the blow up of smooth solutions to the N‐S‐P system. Then we construct a family of analytical solutions that blow up in finite time. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
11.
Weiwei Wang Fei Jiang Zhensheng Gao 《Mathematical Methods in the Applied Sciences》2012,35(9):1014-1032
In this paper, we prove the sequential stability of weak solutions over time, in relation to the Navier–Stokes system of compressible self‐gravitating fluids in a three‐dimensional domain. As a byproduct, we show that there exists at least one non‐negative solution to the stationary problem in any bounded domain with a given mass for the adiabatic constant γ > 3 ∕ 2. In particular, for the spherically symmetric case, these conclusions still hold for γ > 4 ∕ 3 or γ = 4 ∕ 3 with a small mass. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
《Mathematical Methods in the Applied Sciences》2018,41(2):750-768
This paper is dedicated to the study of a family of nonlinear Volterra equations coming from the theory of viscoelasticity. We analyze the existence of local mild solutions to the problem and their possible continuation to a maximal interval of existence. We also consider the problem of continuous dependence with respect to initial data. 相似文献
13.
《Mathematical Methods in the Applied Sciences》2018,41(12):4724-4736
In this paper, we are concerned with the large time behavior of solutions to the Cauchy problem for the one dimensional Navier‐Stokes/Allen‐Cahn system. Motivated by the relationship between the Navier‐Stokes/Allen‐Cahn system and the Navier‐Stokes system, we can prove that the solutions to the one‐dimensional compressible Navier‐Stokes/Allen‐Cahn system tend time‐asymptotically to the rarefaction wave, where the strength of the rarefaction wave is not required to be small. The proof is mainly based on a basic energy method. 相似文献
14.
Jianwei Dong Guangpu Lou Yong Yang 《Mathematical Methods in the Applied Sciences》2019,42(18):7425-7431
In this paper, we will show the blowup of classical solutions to the Cauchy problem for the pressureless Euler/isentropic Navier‐Stokes equations in arbitrary dimensions under some restrictions on the initial data. Compared with the degenerate viscosities appeared in the recent work, we consider the constant viscosities, but we can remove the condition that the adiabatic exponent has a upper bound, which was a key constraint in the proof of the blow‐up result is based on the construction of some new differential inequalities. 相似文献
15.
In this paper, we consider the Navier–Stokes–Poisson equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying p(?)=a?logd (?) for large ?. Here d>1 and a>0. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
Eduard Feireisl Madalina Petcu Dalibor Prak 《Mathematical Methods in the Applied Sciences》2019,42(5):1465-1479
We propose a simple model for a two‐phase flow with a diffuse interface. The model couples the compressible Navier‐Stokes system governing the evolution of the fluid density and the velocity field with the Allen‐Cahn equation for the order parameter. We show that the model is thermodynamically consistent, in particular, a variant of the relative energy inequality holds. As a corollary, we show the weak‐strong uniqueness principle, meaning any weak solution coincides with the strong solution emanating from the same initial data on the life span of the latter. Such a result plays a crucial role in the analysis of the associated numerical schemes. Finally, we perform the low Mach number limit obtaining the standard incompressible model. 相似文献
17.
We study a class of compressible non‐Newtonian fluids in one space dimension. We prove, by using iterative method, the global time existence and uniqueness of strong solutions provided that the initial data satisfy a compatibility condition and the initial density is small in its H1‐norm. The main difficulty is due to the strong nonlinearity of the system and the initial vacuum. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
18.
Global solutions to Keller‐Segel‐Navier‐Stokes equations with a class of large initial data in critical Besov spaces 下载免费PDF全文
Minghua Yang 《Mathematical Methods in the Applied Sciences》2017,40(18):7425-7437
In this article, we consider the Cauchy problem to Keller‐Segel equations coupled to the incompressible Navier‐Stokes equations. Using the Fourier frequency localization and the Bony paraproduct decomposition, let uF:=etΔu0; we prove that there exist 2 positive constants σ0 and C0 such that if the gravitational potential and the initial data (u0,n0,c0) satisfy for some p,q with and , then the global solutions can be established in critical Besov spaces. 相似文献
19.
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
20.
In this paper, we study solvability of the local mild solution of stochastic Navier‐Stokes equation with jump noise in ‐spaces. This research work has mainly carried out by exploiting some interesting works of Tosio Kato. 相似文献