Hausdorff Dimension of Concentration for Isentropic Compressible Navier–Stokes Equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)375–416
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume234
Issue number1
Online published23 Apr 2019
Publication statusPublished - Oct 2019

Abstract

The concentration phenomenon of the kinetic energy, ρ |u|2, associated to isentropic compressible Navier–Stokes equations, is addressed in Rn with = 2, 3 and the adiabatic constant γ ∈ [1, n/2]. Except for a space-time set with a Hausdorff dimension of less than or equal to Γ(n) + 1 with

Γ(n) = max {γ(n), - (/(γ(n) + 1)} and γ(n) = (n(- 1) - )/(γ),

no concentration phenomenon occurs.