Global regularity of a class of p-fluid flows in cylinders

Crispo, Francesca

doi:10.1016/j.jmaa.2007.10.034

Cited by 11 publications

(10 citation statements)

References 14 publications

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“…This derives, technically, from the fact that the boundary prevents from using the difference quotients method in the x 3 (normal) direction. In addition, in the forthcoming paper [9] the author considers the above problem in cylindrical domains, by working in the framework of cylindrical coordinates and by obtaining similar results. Furthermore, the same regularity results of [2] for the boundary value problem in smooth domains are proved in [6].…”

Section: Introduction and Main Resultsmentioning

confidence: 92%

On the W2,q-Regularity of Incompressible Fluids with Shear-Dependent Viscosities: The Shear-Thinning Case

Berselli

2008

J. math. fluid mech.

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In this paper we improve the results stated in Reference [2], in this same Journal, by using -basically-the same tools. We consider a non Newtonian fluid governed by equations with p-structure and we show that second order derivatives of the velocity and first order derivatives of the pressure belong to suitable Lebesgue spaces. (2000). Primary 76A05; secondary 35B65, 35Q35. Mathematics Subject ClassificationKeywords. Shear dependent viscosity, incompressible fluid, regularity up to the boundary.

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Section: Introduction and Main Resultsmentioning

confidence: 92%

On the W2,q-Regularity of Incompressible Fluids with Shear-Dependent Viscosities: The Shear-Thinning Case

Berselli

2008

J. math. fluid mech.

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“…For simplicity, we consider the basic system (1.1). For regularity results, up to the boundary, in W 2,q (Ω)-spaces we refer the reader to [3,6,7,9] and [10]. In [3] and [7] the problem is studied in the "cubic domain" framework considered in the sequel.…”

Section: Introduction and Resultsmentioning

confidence: 99%

On non-Newtonian p-fluids. The pseudo-plastic case

Veiga

2008

Journal of Mathematical Analysis and Applications

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In the following we study a class of stationary Navier-Stokes equations with shear dependent viscosity, under the non-slip (Dirichlet) boundary condition. We consider pseudo-plastic fluids. A fluid is said pseudo-plastic, or shear thinning, if in Eq. (1.1) below one has p < 2. We are interested in global (i.e., up to the boundary) regularity results, in dimension n = 3, for the second order derivatives of the velocity and the first order derivatives of the pressure. We consider a cubic domain Ω and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary.

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“…Finally, we remark that the same improvements also hold in the cases considered in [10,11], where, in the shear thinning fluids case, we deal with the regularity problem for cylindrical boundary domains. Concerning general nonflat boundaries, the extension of the above kind of results presents new obstacles, in comparison with the classical case p = 2.…”

Section: Introductionmentioning

confidence: 78%