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1996 | 33 | 1 | 369-382
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Existence and stability theorems for abstract parabolic equations, and some of their applications

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For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
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  • Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A.
  • Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland
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  • [15] G. Ströhmer, An existence result for partially regular weak solutions of certain abstract evolution equations, with an application to magneto-hydrodynamics, ibid. 213 (1993), 373-385.
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  • [17] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
  • [18] W. von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations, Vieweg, Braunschweig, 1985.
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