Abstract
This paper is concerned with a system of heat equations with hysteresis and Navier–Stokes equations. In Tsuzuki (J Math Anal Appl 423:877–897, 2015) an existence result is obtained for the problem in a 2-dimensional domain with the Navier–Stokes equation in a weak sense. However the result does not include uniqueness for the problem due to the low regularity for solutions. This paper establishes existence and uniqueness in 2- and 3-dimensional domains with the Navier–Stokes equation in a stronger sense. Moreover this work decides required height of regularity for the initial data by introducing the fractional power of the Stokes operator.
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