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Start Over Subject spatially periodic problem

1. Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \to + \infty $ as $p \to +\infty $

Creator:
Bulíček, M., Málek, Josef, and Rajagopal, Kumbakonam R.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
existence, weak solution, incompressible fluid, pressure-dependent viscosity, shear-dependent viscosity, and spatially periodic problem
Language:
English
Description:
Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Maximal regularity of the spatially periodic stokes operator and application to nematic liquid crystal flows

Creator:
Sauer, Jonas
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Stokesova věta, Stokes operator, spatially periodic problem, maximal Lp regularity, nematic liquid crystal flow, quasilinear parabolic equations, 13, and 51
Language:
English
Description:
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal L^{p} regularity of the periodic Laplace and Stokes operators and a local-intime existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group G: = \mathbb{R}^{n - 1} \times \mathbb{R}/L\mathbb{Z} to obtain an R-bound for the resolvent estimate. Then, Weis’ theorem connecting R-boundedness of the resolvent with maximal L^{p} regularity of a sectorial operator applies., Jonas Sauer., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public