Global Solutions to the Generalized Leray- α System with Non- L2(Rn) Initial Data

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Abstract

Due to the intractability of the Navier–Stokes equation, it is common to study approximating equations. Two of the most common of these are the Leray-α equation (which replaces the solution u with (1 - α2L2) u for a Fourier Multiplier L2) and the generalized Navier–Stokes equation (which replaces the viscosity term ν▵ with νL1). In this paper, we use an interpolation based method to prove the existence of global solutions to the generalized Leray-α system with initial data in Lq(Rn) for 2<q<2nn-2 with multipliers are of the form mi(ξ)=|ξ|γigi(|ξ|), where g is (essentially) a logarithm.

Original languageEnglish (US)
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - Jan 1 2019
Externally publishedYes

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Global Solution
Navier-Stokes Equations
Fourier multipliers
Generalized Equation
Logarithm
Multiplier
Viscosity
Interpolate
Term
Form

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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abstract = "Due to the intractability of the Navier–Stokes equation, it is common to study approximating equations. Two of the most common of these are the Leray-α equation (which replaces the solution u with (1 - α2L2) u for a Fourier Multiplier L2) and the generalized Navier–Stokes equation (which replaces the viscosity term ν▵ with νL1). In this paper, we use an interpolation based method to prove the existence of global solutions to the generalized Leray-α system with initial data in Lq(Rn) for 2",
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