7820

7285

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

شش،56ص.

ص.ع.به فارسي و انگليسي

محمدرضا رئوفي

مهدي تاتاري

10/4/92

مجيد گازر، رضا مزروعي سبداني

رياضي

ID7285

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Upper Bounds of the Rates of Decay for Solutions of the Boussinesq Equations Fatemeh Samieesfahani f samieesfahani@math iut ac ir 23 January 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mohammad Reza Raoo raoo @cc iut ac ir Advisor Dr Mehdi Tatari mtatari@cc iut ac ir 2010 MSC 35Q53 35B40 76D05 Keywords the Boussinesq equations L2 decay Fourier splitting method Abstract In this paper upper bounds of the L2 decay rate for the Boussinesq equations are considered Using the L2 decay rate of solutions for the heat equation and assuming that the solutions of the Boussinesq equations are smooth we obtain the upper bounds of L2 decay rate for the smooth solutions and di erence between the solutions of the Boussinesq equations and those of the heat system with the same initial data The decay results may then be obtained by passing to the limit of approximating sequences of solutions The main tool is the Fourier splitting method We consider the large time behavior of solutions to the Cauchy problem for the Boussinesq equations in n space dimensions u u u p u f x t Rn 0 t t u x t Rn 0 div u 0 x t Rn 0 u x 0 u0 x 0 0 x Rn t 0 Here n is space dimensions u u x t is the velocity eld of the ow is the active scalar or temperature p x t is the scalar pressure of the ow f x t is the exteral potential The Boussinesq equations are structurally similar to the Navier Stokes equations in uid dynamics Speci cally when the temperature x t 0 the Bossinesq equations reduce to the incompressible Navier Stokes

محمدرضا رئوفي

مهدي تاتاري

مجيد گازر، رضا مزروعي سبداني