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  • We improve a regularity criterion for the solutions to the Navier-Stokes equations in the full three-dimensional space involving the gradient of one velocity component. Revising the method used in cite{PoZh} and cite{PoZh2}, we show that a weak solution $u$ is regular on $(0,T)$ provided that $nabla u_3 in L^t(0,T;L^s)$, where $2/t+3/s = 19/10$ for $s in [30/19,10/3]$ and $2/t+3/s = 7/4+1/(2s)$ for $s in [10/3,infty]$. It improves the known results for $s in [30/19,150/77)$ and $s in (10/3,infty]$
  • We improve a regularity criterion for the solutions to the Navier-Stokes equations in the full three-dimensional space involving the gradient of one velocity component. Revising the method used in cite{PoZh} and cite{PoZh2}, we show that a weak solution $u$ is regular on $(0,T)$ provided that $nabla u_3 in L^t(0,T;L^s)$, where $2/t+3/s = 19/10$ for $s in [30/19,10/3]$ and $2/t+3/s = 7/4+1/(2s)$ for $s in [10/3,infty]$. It improves the known results for $s in [30/19,150/77)$ and $s in (10/3,infty]$ (en)
Title
  • On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
  • On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component (en)
skos:prefLabel
  • On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
  • On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component (en)
skos:notation
  • RIV/68407700:21110/14:00227613!RIV15-MSM-21110___
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  • 34503
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  • RIV/68407700:21110/14:00227613
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  • Navier-Stokes equations; regularity criteria (en)
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  • NL - Nizozemsko
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  • [049C593407BD]
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  • Nonlinear Analysis: Theory, Methods & Applications
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  • 104
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  • Skalák, Zdeněk
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  • 000335009200007
issn
  • 0362-546X
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  • 10.1016/j.na.2014.03.018
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  • 21110
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