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The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case

Author : H. Beirão da Veiga

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

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Abstract

We consider the p-Laplacian system of N equations in n space variables, 1 < p ≤ 2 , under the homogeneous Navier slip boundary condition without friction. Here, the gradient of the velocity is replaced by the (more physical) symmetric gradient, and the classical non-slip boundary condition is replaced by the Navier slip boundary condition without friction. These combination of circumstances leads to some additional obstacles. We prove W 2, q  regularity, up to the boundary, under suitable assumptions on the couple p, q . The singular case μ = 0 is covered.

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previous chapter A Generalization of Some Regularity Criteria to the Navier–Stokes Equations Involving One Velocity Component
next chapter Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent
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Metadata
Title
On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case
Author
H. Beirão da Veiga
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_6

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