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Navier-Stokes Equations
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TLDR
Schiff's base dichloroacetamides having the formula OR2 PARALLEL HCCl2-C-N ANGLE R1 in which R1 is selected from the group consisting of alkenyl, alkyl, alkynyl and alkoxyalkyl; and R2 is selected by selecting R2 from the groups consisting of lower alkylimino, cyclohexenyl-1 and lower alkynyl substituted cycloenenyl -1 as discussed by the authors.Citations
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Existence of solutions for the Ericksen-Leslie system
Fanghua Lin,Chun Liu +1 more
TL;DR: In this article, the authors study the general Ericksen-Leslie system, which describes the flow of liquid crystal materials, and establish the dissipation property of the system and prove the global existence of weak solutions.
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Partial regularity of the dynamic system modeling the flow of liquid crystals
Fanghua Lin,Chun Liu +1 more
TL;DR: In this paper, the partial regularity of suitable weak solutions to the dynamical systems modelling the flow of liquid crystals is established, which is a natural generalization of an earlier work of Caffarelli-Kohn-Nirenberg on the Navier-Stokes system with some simplifications due to better estimates on the pressure term.
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Existence results for the flow of viscoelastic fluids with a differential constitutive law
C. Guillopé,J. C. Saut +1 more
TL;DR: In this article, the authors define a tensor tensor as a (symmetric) extra-stress tensor, where the total stress is given by g = -pL + I, where p is the hydrodynamic pressure and 4 is the rate of deformation tensor.
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The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part II: Numerical analysis
TL;DR: In this article, a mathematical analysis is carried out for the Cahn-Hilliard equation where the free energy takes the form of a double well potential function with infinite walls, and the existence and uniqueness are proved for a weak formulation of the problem which possesses a Lyapunov functional.
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Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
Youshan Tao,Michael Winkler +1 more
TL;DR: In this paper, it was shown that for arbitrarily large initial data, this problem admits at least one global weak solution for which there exists T > 0 such that ( u, v ) is bounded and smooth in Ω × (T, ∞ ).