EXISTENCE OF PERIODIC SOLUTIONS OF THE EQUATIONS OF INCOMPRESSIBLE MICROSTRETCH FLUID FLOW

Abstract

involving of Mathematics, flow of incompressible the velocity vector RAO and K. VENKATAPATHI Regional microstretch Engineering College, fluid is governed RAJU Warangal-506004, India by a system of differential cf. the microprotation of the fluid element. vector f and the scalar Y representing equations the microstretch Let R = R(t) be a bounded domain in space and let the field (Q, 6, v) be prescribed at each point of the boundary aR(t). If the domain R(r) and the boundary data depend periodically 1, it is shown that under some assumptions on the initial distribution of on the time the flow fields and the material constants R(r), of the fluid, there exists a unique, stable, periodic solution of the microstretch taking the prescribed values on the boundary dR(t) (Theorem flow equations in 2 of the paper). The proof rests on some relations describing microstretch the rate of decay of the energy functionals corresponding to the difference of two flows in the domain that have the same density and gyration parameters and are subject to the same boundary conditions.