Modified Boussinesq System with Variable Coefficients： Classical Lie Approach and Exact Solutions
Modified Boussinesq System with Variable Coefficients： Classical Lie Approach and Exact Solutions
摘要
The Lie-group formalism is applied to investigate the symmetries of the modified Boussinesq system with variable coefficients. We derived the infinitesimals and the admissible forms of the coefficients that admit the classical symmetry group. The reduced systems of ordinary differential equations deduced from the optimal system of subalgebras are further studied and some exact solutions are obtained.
二级参考文献10
-
1Tanner R I. Plane creeping flow of incompressible second order fluids [ J ]. Phys Fluids, 1996, 9:1246.
-
2Huilgol R R. On uniqueness and non-uniqueness in the plane creeping flows of second order fluids[J]. Soc IndAppl, 1973,24:226.
-
3Fosdick R L, Rajagopal K R. Uniqueness and drag for fluids of second grade in steady motion[ J]. Internat J Non-Linear Mech , 1978,13:131.
-
4Rajagopal K R. On the creeping flow of the second-order fluids[ J]. J Non-Newtonian Fluid Mech,1984,15:239.
-
5Dunn J E, Rajagopal K R. Fluids of differential type: critical review and thermodynamic analysis[ J].Internat J Engng Sci, 1995,33:689.
-
6Bourgin P, Tichy J A. The effect of an additional boundary condition on the plane creeping flow of a second-order fluid[ J]. Internat J Non-Linear Mech , 1989,24:561.
-
7Galdi G P , Rajagopal K R. Slow motion of a body in a fluid of second grade [ J ] . Internat J Engng Sci, 1997,35:33.
-
8Bluman G W,Kumei S. Symmetries and DifferentialEquations [M]. New York: Springer, 1989.
-
9Dunn J E, Fosdick R L. Thermodynamics stability and boundedness of fluids complexity 2 and fluids of second grade[ J]. Arch Rational Mech Anal, 1971,56:191.
-
10Rajagopal K R. On the boundary conditions for fluids of the differential type[ A]. In: Navier-Stokes Equations and Related Nonlinear Problems [ C] .New York:Plenum Press, 1994.
共引文献3
-
1Asif Aii,Ahmer Mehmood,Muhammad R.Mohyuddin.Lie group analysis of viscoelastic MHD aligned flow and heat transfer[J].Acta Mechanica Sinica,2005,21(4):342-345.
-
2张道祥,冯素晓,卢志明,刘宇陆.Application of diflerential constraint method to exact solution of second-grade fluid[J].Applied Mathematics and Mechanics(English Edition),2009,30(4):403-412.
-
3张道祥,冯素晓,卢志明,刘宇陆.微分约束方法在求解二阶流体精确解上的应用[J].应用数学和力学,2009,30(4):379-387. 被引量：1
-
1SU Xing,CAO Jie,ZHANG Jian-lin.A Remark on Persistence of Regularity for the Nonlinear Boussinesq System in Dimension Two[J].Chinese Quarterly Journal of Mathematics,2016,31(1):102-110.
-
2LI JiBin.Bifurcations of travelling wave solutions for two generalized Boussinesq systems[J].Science China Mathematics,2008,51(9):1577-1592. 被引量：4
-
3CUI Xiaona,DOU Changsheng,JIU Quansen.Local Well-Posedness and Blow Up Criterion for the Inviscid Boussinesq System in Holder Spaces[J].Journal of Partial Differential Equations,2012,25(3):220-238. 被引量：4
-
4张善卿,徐桂琼.General explicit solutions of a classical Boussinesq system[J].Chinese Physics B,2002,11(10):993-995. 被引量：2
-
5李宏哲,田播,李丽莉,张海强.Painlevé Analysis and Darboux Transformation for a Variable-Coefficient Boussinesq System in Fluid Dynamics with Symbolic Computation[J].Communications in Theoretical Physics,2010(5):831-836.
-
6ZHI Hong-Yan,ZHAO Xue-Qin,ZHANG Hong-Qing.New Approach to Find Exact Solutions to Classical Boussinesq System[J].Communications in Theoretical Physics,2005,44(4X):597-603.
-
7LI Lin-rui,WANG Ke,HONG Ming-li.The Asymptotic Limit for the 3D Boussinesq System[J].Chinese Quarterly Journal of Mathematics,2016,31(1):51-59. 被引量：1
-
8TIANYong－Bo CHENGYi 等.Formulas to Solve the （2＋1）—Dimensional System：The （2＋1）—Extension of Classical Boussinesq System[J].Communications in Theoretical Physics,2001,35(5):519-522.
-
9Jian-guo SHI,Shu WANG,Ke WANG,Feng-ying HE.The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection[J].Acta Mathematicae Applicatae Sinica,2014,30(1):75-88.
-
10SHI Jian-guo WU Zhong-lin.The limit of the Boussinesq system of Rayleigh-Bénard convection as the Prandtl number approaches infinity[J].Applied Mathematics(A Journal of Chinese Universities),2011,26(4):493-502.
