Critical Function Spaces for the Wellposedness of the Navier-Stokes Initial Value Problem

Gallagher, Isabelle

doi:10.1007/978-3-319-10151-4_12-1

Cited by 2 publications

(1 citation statement)

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“…The error estimates in the above-mentioned articles all require the initial value to be strictly smoother than L2 , which is known to be a critical space for the 2D NS equations, a maximal Sobolev space on which well-posedness of the 2D NS equations is proved; see [13]. As a result, the error analysis in this case turns out to be much more challenging than that for smoother initial data.…”

Section: Of Chapter 3]mentioning

confidence: 99%

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Ueda

2022

ESAIM: M2AN

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First-order convergence in time and space is proved for a fully discrete semi- implicit finite element method for the two-dimensional Navier–Stokes equations with L 2 ini- tial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier–Stokes equations in the analysis of the consistency errors, an appropriate duality argument, and the smallness of the numerical solution in the discrete L 2 ( 0 ,t m ; H 1 ) norm when t m is smaller than some constant. Numerical examples are provided to support the theoretical analysis.

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Section: Of Chapter 3]mentioning

confidence: 99%

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Ueda

2022

ESAIM: M2AN

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Analysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data

Li¹,

Ma²,

Ueda³

2021

Preprint

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First-order convergence in time and space is proved for a fully discrete semiimplicit finite element method for the two-dimensional Navier-Stokes equations with L 2 initial data in convex polygonal domains, without extra regularity assumptions or grid-ratio conditions. The proof utilises the smoothing properties of the Navier-Stokes equations in the analysis of the consistency errors, an appropriate duality argument, and the smallness of the numerical solution in the discrete L 2 (0, tm; H 1 ) norm when tm is smaller than some constant. Numerical examples are provided to support the theoretical analysis.

show abstract

Critical Function Spaces for the Wellposedness of the Navier-Stokes Initial Value Problem

Cited by 2 publications

References 94 publications

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Analysis of fully discrete finite element methods for 2D Navier–Stokes equations with critical initial data

Analysis of fully discrete finite element methods for 2D Navier--Stokes equations with critical initial data

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