Abstract.
We describe a new approach to the study of initial-boundary value problems for evolutionary equations of hydrodynamics, which is based on approximation of the problems and subsequent application of topological degree theory for investigation of weak solvability for approximating problems. Use of this method turned out to be especially effective in problems of non- Newtonian hydrodynamics. We demonstrate its application to the study of weak solvability and attractors of the initial-boundary value problem for the Oldroyd model with regularized objective Jaumann derivative.
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Zvyagin, V.G., Vorotnikov, D.A. Approximating-topological methods in some problems of hydrodynamics. J. fixed point theory appl. 3, 23–49 (2008). https://doi.org/10.1007/s11784-008-0056-7
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DOI: https://doi.org/10.1007/s11784-008-0056-7