Abstract
For a Navier–Stokes–Nernst–Planck–Poisson system we construct global weak solutions in a three-dimensional bounded domain. A special feature of our approach is that we allow for nonconstant diffusion coefficients which may vary from species to species as well as for \({L^2}\)-initial data without any further constraints. Our approach is based on the intrinsic energy structure, Aubin–Simon compactness arguments, and maximal \({L^p}\)-regularity.
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Dedicated to Professor Jan Prüss on the occasion of his 65th birthday.
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Fischer, A., Saal, J. Global weak solutions in three space dimensions for electrokinetic flow processes. J. Evol. Equ. 17, 309–333 (2017). https://doi.org/10.1007/s00028-016-0356-0
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DOI: https://doi.org/10.1007/s00028-016-0356-0