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This paper is concerned with a system of heat equations with hysteresis and NavierStokes equations in two-dimensional domains. There are some studies on the system of heat equations and Navier-Stokes equations in which the temperature (the solution to heat equations) is controlled by obstacle functions. In this paper, the control of the temperature is precisely described by introducing hysteresis. This paper provides the existence of solutions along the abstract theory for evolution equations with subdifferential operators.

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