Immiscible Fluids and Chemotaxis
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This second part is devoted to a series of three applications of the method of intrinsic scaling to relevant models arising from flows in porous media, chemotaxis and phase transitions.
We start with the flow of two immiscible fluids through a porous medium, proving the Hölder continuity of the saturations, which satisfy a PDE with a two-sided degeneracy. The same type of structure arises in a model for the chemotactic movement of cells under a volume-filling effect and the extension to this case, which basically consists in dealing appropriately with an extra lower order term, is also included.
KeywordsPorous Medium Time Level Piecewise Smooth Immiscible Fluid Iteration Technique
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