PERISTALTIC TRANSPORT OF A HEAT-CONDUCTING VISCOUS-FLUID AS AN APPLICATION OF ABSTRACT DIFFERENTIAL-EQUATIONS AND SEMIGROUP OF OPERATORS

A recent abstract result of Rankin (Trans. Amer. Math. Soc., to appear) is applied to the peristaltic transport of a heat-conducting fluid in a flexible tube. The Oberbeck-Boussinesq equations are used as the governing equations, a pressure drop over a wavelength of the tube is prescribed to ensure uniqueness, and Newton's cooling law for the temperature is imposed on the boundary. With the notion of a weak solution introduced, local existence, uniqueness, regularity, and continuation of solutions are considered; in particular, Wr2(Ω) regularity of the solutions is established. © 1992.