The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure

Jiří Neustupa

Applications of Mathematics (2003)

  • Volume: 48, Issue: 6, page 547-558
  • ISSN: 0862-7940

Abstract

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We assume that 𝕧 is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of 𝕧 near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of 𝕧 .

How to cite

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Neustupa, Jiří. "The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure." Applications of Mathematics 48.6 (2003): 547-558. <http://eudml.org/doc/33167>.

@article{Neustupa2003,
abstract = {We assume that $\{\mathbb \{v\}\}$ is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of $\{\mathbb \{v\}\}$ near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of $\{\mathbb \{v\}\}$.},
author = {Neustupa, Jiří},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; regularity; Navier-Stokes equations; conditions of Prodi-Serrin type},
language = {eng},
number = {6},
pages = {547-558},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure},
url = {http://eudml.org/doc/33167},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Neustupa, Jiří
TI - The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 6
SP - 547
EP - 558
AB - We assume that ${\mathbb {v}}$ is a weak solution to the non-steady Navier-Stokes initial-boundary value problem that satisfies the strong energy inequality in its domain and the Prodi-Serrin integrability condition in the neighborhood of the boundary. We show the consequences for the regularity of ${\mathbb {v}}$ near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of ${\mathbb {v}}$.
LA - eng
KW - Navier-Stokes equations; regularity; Navier-Stokes equations; conditions of Prodi-Serrin type
UR - http://eudml.org/doc/33167
ER -

References

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