Finite energy of generalized suitable weak solutions to the Navier–Stokes equations and Liouville-type theorems in two dimensional domains

Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi

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    Abstract

    Introducing a new notion of generalized suitable weak solutions, we first prove validity of the energy inequality for such a class of weak solutions to the Navier–Stokes equations in the whole space Rn. Although we need certain growth condition on the pressure, we may treat the class even with infinite energy quantity except for the initial velocity. We next handle the equation for vorticity in 2D unbounded domains. Under a certain condition on the asymptotic behavior at infinity, we prove that the vorticity and its gradient of solutions are both globally square integrable. As their applications, Loiuville-type theorems are obtained.

    Original languageEnglish
    JournalJournal of Differential Equations
    DOIs
    Publication statusAccepted/In press - 2018 Jan 1

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    Keywords

    • Energy inequalities
    • Liouville-type theorems
    • Navier–Stokes equations

    ASJC Scopus subject areas

    • Analysis

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