Global existence and regularity for the dynamics of viscous oriented fluids

Luca Bisconti; Paolo Maria Mariano; Luca Bisconti; Paolo Maria Mariano

doi:10.3934/math.2020006

AIMS Mathematics

2020, Volume 5, Issue 1: 79-95. doi: 10.3934/math.2020006

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Global existence and regularity for the dynamics of viscous oriented fluids

Luca Bisconti ¹,
Paolo Maria Mariano ^{2
,
,}

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

Received: 22 July 2019 Accepted: 10 October 2019 Published: 18 October 2019
MSC : 35L65, 74N15, 76D03, 76D05

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.
- 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[J]. AIMS Mathematics, 2020, 5(1): 79-95. doi: 10.3934/math.2020006

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Abstract

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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