Dynamics of fluids flows under Markovian structural perturbations. (English) Zbl 1121.76019
Summary: We investigate dynamics of plane flows and three-dimensional flows of an incompressible viscous Newtonian fluids under Markovian structural perturbations. We employ the theory of random partial differential inequalities together with the concept of vector Lyapunov-like functionals to investigate different kinds of stability and convergence properties of the solution process of the model and characterize the effects of the random structural perturbations on convergence and stability.
MSC:
| 76D06 | Statistical solutions of Navier-Stokes and related equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 76E05 | Parallel shear flows in hydrodynamic stability |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
Keywords:
differential inequalities; Lyapunov-like functional; comparison theorem; convergence and stabilityReferences:
| [1] | Georgescu, A., Hydronamic Stability Theory (1985), Martinus Nijhoff Publishers: Martinus Nijhoff Publishers New York |
| [2] | Ladde, G. S.; Lakshmikantham, V., Random Differential Inequalities (1980), Academic Press: Academic Press Boston, MA · Zbl 0466.60002 |
| [3] | Ladde, G. S.; Lakshmikantham, V.; Liu, P. T., Differential inequalities and boundedness of stochastic differential equations, Journal of Mathematical Analysis and Applications, 48, 2 (1974) · Zbl 0295.60043 |
| [4] | Anabtawi, M. J.; Ladde, G. S., Convergence and stability analysis of system of partial differential equations under Markovian structural perturbations II-vector Lyapunov-like functionals, Journal of Stochastic Analysis and Applications, 18, 671-696 (2000) · Zbl 0972.60051 |
| [5] | Lu, P. C., Introduction to the Mechanics of Viscous Fluids (1977), Hemisphere Publishing Corporation: Hemisphere Publishing Corporation New York |
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