Linear flow problems in 2D exterior domains for 2D incompressible fluid flows

Konieczny, Paweł

doi:10.4064/bc81-0-16

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Proof Of Theorem 111

The Kernel Function ψ1

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2008

2009

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Cited by 2 publications

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“…), since then one may use standard techniques for Hilbert spaces. We refer the Reader to [15], where a similar linear problem is considered and using these results we are able to show existence also for the Oseen system in an elementary way.…”

Section: Proof Of Theorem 11mentioning

confidence: 85%

Thorough analysis of the Oseen system in 2D exterior domains

Konieczny

2009

Math Methods in App Sciences

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Abstract. We construct L p -estimates for the inhomogeneous Oseen system studied in a two dimensional exterior domain Ω with inhomogeneous slip boundary conditions. The kernel of the paper is a result for the half space R 2 + . Analysis of this model system shows us a parabolic character of the studied problem, resulting as an appearance of the wake region behind the obstacle. Main tools are given by the Fourier analysis to obtain the maximal regularity estimates. The results imply the solvability for the Navier-Stokes system for small velocity at infinity. MSC: 35Q30, 75D07

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Section: Proof Of Theorem 11mentioning

confidence: 85%

Thorough analysis of the Oseen system in 2D exterior domains

Konieczny

2009

Math Methods in App Sciences

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“…In [13] it is shown that also for an exterior domain a family of solutions to a similar problem is also one dimensional. In that case, however, one needs to use additional property for a solution v, namely v → 0 as |x| → ∞.…”

Section: The Kernel Function ψmentioning

confidence: 97%