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Global existence and regularity for the dynamics of viscous oriented fluids

1 DIMAI, Università di Firenze, viale Morgagni 67/a, I-50134 Firenze, Italy
2 DICEA, Universita di Firenze, via Santa Marta 3, I-50136 Firenze, Italy

Special Issues: Initial and Boundary Value Problems for Differential Equations

We prove global existence of weak solutions to regularized versions of balance equations representing the dynamics over a torus of complex fluids, with microstructure described by a vector field taking values in the unit ball. Regularization is offered by the presence of second-neighbor microstructural interactions and our choice of filtering the balance of macroscopic momentum by inverse Helmholtz operator with unit length scale.
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Keywords mechanics of complex materials; spin fluids; second-neighbor interactions; hyperbolic equations

Citation: Luca Bisconti, Paolo Maria Mariano. Global existence and regularity for the dynamics of viscous oriented fluids. AIMS Mathematics, 2020, 5(1): 79-95. doi: 10.3934/math.2020006


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