2015
DOI: 10.1007/s00021-015-0210-0
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Existence and Uniqueness of Solutions to Heat Equations with Hysteresis Coupled with Navier–Stokes Equations in 2D and 3D

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. Moreove… Show more

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