共查询到20条相似文献,搜索用时 15 毫秒
1.
A random perturbation of a deterministic Navier?CStokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term ${u{\nabla}u}$ . This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier?CStokes equation. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron?CMartin version of the Wiener chaos expansion. It is shown that the generalized solution is a Markov process and scales effectively by Catalan numbers. 相似文献
2.
Huabin Chen 《Proceedings Mathematical Sciences》2012,122(2):283-295
The paper proves the L 2-exponential stability of weak solutions of two-dimensional stochastic Navier?CStokes equations in the presence of delays. The results extend some of the existing results. 相似文献
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For 2-D stochastic Navier-Stokes equations on the torus with multiplicative noise we construct a perfect cocycle and show
the existence of global random compact attractors. The equations considered do not admit a pathwise method of solution.
Received: 9 June 1998 / Revised version: 17 December 1998 相似文献
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《Journal de Mathématiques Pures et Appliquées》2003,82(8):877-947
We consider the Kolmogorov equation associated with the stochastic Navier–Stokes equations in 3D, we prove existence of a solution in the strict or mild sense. The method consists in finding several estimates for the solutions um of the Galerkin approximations of u and their derivatives. These estimates are obtained with the help of an auxiliary Kolmogorov equation with a very irregular negative potential. Although uniqueness is not proved, we are able to construct a transition semigroup for the 3D Navier–Stokes equations. Furthermore, this transition semigroup has a unique invariant measure, which is ergodic and strongly mixing. 相似文献
5.
Loeb space methods are used to prove existence of an optimal control for general 3D stochastic Navier–Stokes equations with multiplicative noise. The possible non-uniqueness of the solutions mean that it is necessary to utilize the notion of a non-standard approximate solution developed in the paper by N.J. Cutland and Keisler H.J. 2004, Global attractors for 3-dimensional stochastic Navier–Stokes equations, Journal of Dynamics and Differential Equations, pp. 16205–16266, for the study of attractors. 相似文献
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In this paper we prove the convergence of stochastic Navier–Stokes equations driven by white noise. A linearized version of the implicit Crank–Nicolson scheme is considered for the approximation of the solutions to the N–S equations. The noise is defined as the distributional derivative of a Wiener process and approximated by using the generalized L2-projection operator. Optimal strong convergence error estimates in the L2 norm are obtained. 相似文献
9.
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
10.
Martin Hairer Jonathan C. Mattingly Étienne Pardoux 《Comptes Rendus Mathematique》2004,339(11):793-796
This Note mainly presents the results from “Malliavin calculus and the randomly forced Navier–Stokes equation” by J.C. Mattingly and E. Pardoux. It also contains a result from “Ergodicity of the degenerate stochastic 2D Navier–Stokes equation” by M. Hairer and J.C. Mattingly. We study the Navier–Stokes equation on the two-dimensional torus when forced by a finite dimensional Gaussian white noise. We give conditions under which the law of the solution at any time , projected on a finite dimensional subspace, has a smooth density with respect to Lebesgue measure. In particular, our results hold for specific choices of four dimensional Gaussian white noise. Under additional assumptions, we show that the preceding density is everywhere strictly positive. This Note's results are a critical component in the ergodic results discussed in a future article. To cite this article: M. Hairer et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
11.
The backward two-dimensional stochastic Navier–Stokes equations (BSNSEs, for short) with suitable perturbations are studied in this paper, over bounded domains for incompressible fluid flow. A priori estimates for adapted solutions of the BSNSEs are obtained which reveal a pathwise L∞(H) bound on the solutions. The existence and uniqueness of solutions are proved by using a monotonicity argument for bounded terminal data. The continuity of the adapted solutions with respect to the terminal data is also established. 相似文献
12.
Spatially homogeneous solutions of 3D stochastic Navier–Stokes equations and local energy inequality
We study the three-dimensional stochastic Navier–Stokes equations with additive white noise, in the context of spatially homogeneous solutions in R3, i.e. solutions with a law invariant under space translations. We prove the existence of such a solution, with the additional property of being suitable in the sense of Caffarelli, Kohn and Nirenberg: it satisfies a localized version of the energy inequality. 相似文献
13.
Zdzisław Brzeźniak Gaurav Dhariwal Mauro Mariani 《Journal of Differential Equations》2018,264(4):2833-2864
We study 2D Navier–Stokes equations with a constraint forcing the conservation of the energy of the solution. We prove the existence and uniqueness of a global solution for the constrained Navier–Stokes equation on and , by a fixed point argument. We also show that the solution of the constrained equation converges to the solution of the Euler equation as the viscosity ν vanishes. 相似文献
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Cung The Anh Nguyen Van Thanh 《Stochastics An International Journal of Probability and Stochastic Processes》2019,91(4):485-513
We consider the 3D stochastic Navier–Stokes–Voigt equations in bounded domains with the homogeneous Dirichlet boundary condition and infinite-dimensional Wiener process. First, we prove the existence and uniqueness of solutions to the problem. Then we investigate the mean square exponential stability and the almost sure exponential stability of the stationary solutions. 相似文献
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L. I. Rubina O. N. Ul’yanov 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):163-174
We discuss the initial and boundary value problems for the system of dimensionless Navier–Stokes equations describing the dynamics of a viscous incompressible fluid using the method of characteristics and the geometric method developed by the authors. Some properties of the formulation of these problems are considered. We study the effect of the Reynolds number on the flow of a viscous fluid near the surface of a body. 相似文献
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We prove the existence of weak solutions of stochastic Navier–Stokes equation on a two-dimensional torus, which appears in a certain variational problem. Our equation does not satisfy the coercivity condition. We construct its weak solutions due to an approximation by a sequence of solutions of equations with enlarged viscosity terms and then by showing an a priori estimate for them. 相似文献
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In this paper, the blood flow problem is considered in a blood vessel, and a coupling system of Navier–Stokes equations and linear elastic equations, Navier–Lame equations, in a cylinder with cylindrical elastic shell is given as the governing equations of the problem. We provide two finite element models to simulating the three-dimensional Navier–Stokes equations in the cylinder while the asymptotic expansion method is used to solving the linearly elastic shell equations. Specifically, in order to discrete the Navier–Stokes equations, the dimensional splitting strategy is constructed under the cylinder coordinate system. The spectral method is adopted along the rotation direction while the finite element method is used along the other directions. By using the above strategy, we get a series of two-dimensional-three-components (2D-3C) fluid problems. By introduce the S-coordinate system in E3 and employ the thickness of blood vessel wall as the expanding parameter, the asymptotic expansion method can be established to approximate the solution of the 3D elastic problem. The interface contact conditions can be treated exactly based on the knowledge of tensor analysis. Finally, numerical test shows that our method is reasonable. 相似文献
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Theoretical and Mathematical Physics - We present an analysis of the Navier–Stokes equations in the framework of an algebraic approach to systems of partial differential equations (the formal... 相似文献