The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics

Eduard Feireisl; Šárka Matušů-Nečasová

Applications of Mathematics (2011)

  • Volume: 56, Issue: 1, page 39-49
  • ISSN: 0862-7940

Abstract

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The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.

How to cite

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Feireisl, Eduard, and Matušů-Nečasová, Šárka. "The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics." Applications of Mathematics 56.1 (2011): 39-49. <http://eudml.org/doc/116503>.

@article{Feireisl2011,
abstract = {The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.},
author = {Feireisl, Eduard, Matušů-Nečasová, Šárka},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes system; rough boundary; slip boundary condition; Navier-Stokes system; rough boundary; slip boundary condition},
language = {eng},
number = {1},
pages = {39-49},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics},
url = {http://eudml.org/doc/116503},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Feireisl, Eduard
AU - Matušů-Nečasová, Šárka
TI - The effective boundary conditions for vector fields on domains with rough boundaries: Applications to fluid mechanics
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 39
EP - 49
AB - The Navier-Stokes system is studied on a family of domains with rough boundaries formed by oscillating riblets. Assuming the complete slip boundary conditions we identify the limit system, in particular, we show that the limit velocity field satisfies boundary conditions of a mixed type depending on the characteristic direction of the riblets.
LA - eng
KW - Navier-Stokes system; rough boundary; slip boundary condition; Navier-Stokes system; rough boundary; slip boundary condition
UR - http://eudml.org/doc/116503
ER -

References

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  2. Bucur, D., Feireisl, E., Nečasová, Š., 10.1007/s00021-007-0242-1, J. Math. Fluid Mech. 10 (2008), 554-568. (2008) Zbl1189.35219MR2461251DOI10.1007/s00021-007-0242-1
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  4. Bucur, D., Feireisl, E., Nečasová, Š., Wolf, J., 10.1016/j.jde.2008.02.040, J. Differ. Equations 244 (2008), 2890-2908. (2008) Zbl1143.35080MR2418180DOI10.1016/j.jde.2008.02.040
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  7. Jaeger, W., Mikelić, A., 10.1006/jdeq.2000.3814, J. Differ. Equations 170 (2001), 96-122. (2001) Zbl1009.76017MR1813101DOI10.1006/jdeq.2000.3814
  8. Koch, H., Solonnikov, V. A., 10.1023/A:1011375706754, J. Math. Sci. 106 (2001), 3042-3072. (2001) Zbl0987.35121MR1906033DOI10.1023/A:1011375706754
  9. Nitsche, J. A., 10.1051/m2an/1981150302371, RAIRO, Anal. Numér. 15 (1981), 237-248. (1981) Zbl0467.35019MR0631678DOI10.1051/m2an/1981150302371
  10. Sohr, H., The Navier-Stokes Equations. An Elementary Functional Analytic Approach, Birkhäuser Basel (2001). (2001) Zbl0983.35004MR1928881
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