检索结果-南通市图书馆

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2005年第6期21卷 1337-1350页

作者： Chang Xing MIAO Han YANG Institute of Applied Physics and Computational Mathematics P. O. Box 8009 Beijing 100088 P. R. China Department of Mathematics Southwest Jiaotong University Chengdu 610031 P. R. China

In this paper we study the self-similar solution to a class of nonlinear integro-differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space-time estimates which were established by Hirata and Miao in [1] we prove the global existence of self-similar solution of Cauchy problem for the nonlinear integro-differential equation in C＊（[0,∞];B^8pp,∞（R^n）.

关键词： self-similar solution Space-time estimates Integro-differential equation Fractional order time derivative Mittag-Lettter's function Cauchy problem

Local L^(2) theory of the fractional Navier-Stokes equations and the self-similar solution

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2023年第3期66卷 503-570页

作者： Baishun Lai Jingyue Li Xiaoxin Zheng Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Mathematical Sciences Beihang UniversityBeijing 100191China

This paper is concerned with two aspects of the fractional Navier-Stokes equation. First, we establish the local L^(2)theory of the hypo-dissipative Navier-Stokes system. More precisely, the existence of local-in-time as well as global-in-time local energy weak solutions to the hypo-dissipative Navier-Stokes system is *** particular, in order to construct a pressure with an explicit representation, some technical innovations are required due to the lack of known results on the local regularity of the non-local Stokes operator. Secondly, as an important application to the local L^(2)theory, we give a second construction of large self-similar solutions of the hypo-dissipative Navier-Stokes system along with the Leray-Schauder degree theory.

关键词： local energy weak solution self-similar solution Leray-Schauder degree theory

Shock Formation for 2D Isentropic Euler Equations with self-similar Variables

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2024年第3期45卷 349-412页

作者： Wenze SU School of Mathematical Sciences Fudan UniversityShanghai 200433China

The author studies the 2D isentropic Euler equations with the ideal gas *** exhibits a set of smooth initial data that give rise to shock formation at a single point near the planar *** solutions to the 2D isentropic Euler equations are associated with non-zero vorticity at the shock and have uniform-in-time-1/3-Holder ***,these point shocks are of self-similar type and share the same profile,which is a solution to the 2D self-similar Burgers *** proof of the solutions,following the 3D construction of Buckmaster,Shkoller and Vicol(in 2023),is based on the stable 2D self-similar Burgers profile and the modulation method.

关键词： 2D isentropic Euler equations Shock formation self-similar solution

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2011年第11期32卷 1447-1456页

作者： J.HAUSSERMANN K.VAJRAVELU R.A.VAN GORDER Department of Mathematics University of Central Florida P.O.Box 161364OrlandoFlorida 32816-1364USA

The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.

关键词： Lin-Reissner-Tsien equation self-similar solution transonic approximation,nonlinear partial differential equation

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2011年第10期56卷 745-750页

作者： I.F.Barna KFKI Atomic Energy Research Institute of the Hungarian Academy of Sciences Thermohydraulics Department(KFKI-AEKI)H-1525 BudapestP.O.Box 49Hungary

In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.

关键词： Navier-Stokes equation self-similar solution

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 1997年第2期17卷 180-189页

作者：严国政

In this paper, we investigate the following partial differential equation, ut , where a > 0 and p> 1. When n(p-1)/2 > 1 andp > 3, we obtained a nontrivial non-negative global solution. Furthermore, on Sobolev space W1,s(W2,s) with s > 1. a nonuniqueness result is established which shows that there exists a positive solution u(t,x) with u(t,x)→0 as t→0 in W1,s(W2,s). On the other hand, our result can be regarded as a generalization of conclusion of Haraux, *** Weissler, F.B. in [5].

关键词： Existence and asymptotic behavior self-similar solution non-uniqueness

Existence of the self-similar solutions in the heat flow of harmonic maps

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 1999年第2期42卷 113-132页

作者：范辉军 Institute of Mathematics Peking University Beijing China

It is proved that the heat equations of harmonic maps have self-similar solutions satisfying certain energy condition.

关键词： harmonlc map heat flow self-similar solution existence

An Exact solution to the Two-Particle Boltzmann Equation System for Maxwell Gases

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2012年第10期58卷 565-568页

作者：布仁满都拉赵迎春 School of Mathematics and Statistics Chifeng University Primary Education College Chifeng University

An exact solution to the two-particle Boltzmann equation system for Maxwell gases is obtained with use of Bobylev *** relationship between the exact solution and the self-similar solution of the boltzmann equation is ... 详细信息

关键词： the two-particle Boltzmann equation system self-similar solution exact solution

BESOV SPACES AND self-similar solutionS FOR NONLINEAR EVOLUTION EQUATIONS

在线全文

学校读者我要写书评

暂无评论

Journal of Partial Differential Equations 2006年第1期19卷 26-47页

作者： Miao Changxing Zhang Bo Institute of Applied Physics and Computational Mathematics PO Box 8009 Beijing 100088 China Institute of Applied Mathematics Chinese Academy of Sciences Beijing 100080 China School of MIS Coventry University Coventry CV1 5FB UK

In this paper, we establish the existence of global self-similar solutions for the heat and convection-diffusion equations. This we do in some homogeneous Besov spaces using the theory of Besov spaces and the Strichartz estimates. Further, the structure of the self-similar solutions has also been established by using an equivalent norm for Besov spaces.

关键词： Strichartz estimates admissible triplet self-similar solution Besov spaces evolution equations, well-posedness.