Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics

Dominic Breit; Andrea Cianchi

doi:10.1016/j.jde.2015.01.041

Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics

Dominic Breit, Andrea Cianchi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.

Original language	English
Pages (from-to)	48-83
Journal	Journal of Differential Equations
Volume	259
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2015.01.041
Publication status	Published - 2014

Keywords

Bogovskiĭ operator
Negative norms
Non-Newtonian fluids
Orlicz-Sobolev spaces
Singular integrals
Strongly nonlinear elliptic systems

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10.1016/j.jde.2015.01.041

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title = "Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics",

abstract = "We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.",

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journal = "Journal of Differential Equations",

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T1 - Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics

AU - Breit, Dominic

AU - Cianchi, Andrea

PY - 2014

Y1 - 2014

N2 - We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.

AB - We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of boundedness properties of the Bogovskiĭ operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the problem of pressure reconstruction for non-Newtonian fluids governed by constitutive laws, which are not necessarily of power type, are presented. A key inequality for a numerical analysis of the underlying elliptic system is also derived.

KW - Bogovskiĭ operator

KW - Negative norms

KW - Non-Newtonian fluids

KW - Orlicz-Sobolev spaces

KW - Singular integrals

KW - Strongly nonlinear elliptic systems

U2 - 10.1016/j.jde.2015.01.041

DO - 10.1016/j.jde.2015.01.041

M3 - Article

SN - 0022-0396

VL - 259

SP - 48

EP - 83

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Negative Orlicz-Sobolev norms and strongly nonlinear systems in fluid mechanics

Abstract

Keywords

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