Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality
Bollettino dell'Unione Matematica Italiana (2012)
- Volume: 5, Issue: 2, page 225-232
- ISSN: 0392-4041
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topBeirão da Veiga, H.. "Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality." Bollettino dell'Unione Matematica Italiana 5.2 (2012): 225-232. <http://eudml.org/doc/290875>.
@article{BeirãodaVeiga2012,
abstract = {We consider the initial boundary value problem for the 3D Navier-Stokes equations under a slip type boundary condition. Roughly speaking, we are concerned with regularity results, up to the boundary, under suitable assumptions on the directions of velocity and vorticity. Our starting point is a recent, interesting, result obtained by Berselli and Córdoba concerning the ``near orthogonal case''. We also consider a ``near parallel case''.},
author = {Beirão da Veiga, H.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {225-232},
publisher = {Unione Matematica Italiana},
title = {Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality},
url = {http://eudml.org/doc/290875},
volume = {5},
year = {2012},
}
TY - JOUR
AU - Beirão da Veiga, H.
TI - Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/6//
PB - Unione Matematica Italiana
VL - 5
IS - 2
SP - 225
EP - 232
AB - We consider the initial boundary value problem for the 3D Navier-Stokes equations under a slip type boundary condition. Roughly speaking, we are concerned with regularity results, up to the boundary, under suitable assumptions on the directions of velocity and vorticity. Our starting point is a recent, interesting, result obtained by Berselli and Córdoba concerning the ``near orthogonal case''. We also consider a ``near parallel case''.
LA - eng
UR - http://eudml.org/doc/290875
ER -
References
top- BEIRÃO DA VEIGA, H., Direction of vorticity and regularity up to the boundary. The Lipschitz-continuous case, J. Math. Fluid Mech., DOI: 10.1007/s00021-012-0099-9. MR3020905DOI10.1007/s00021-012-0099-9
- BEIRÃO DA VEIGA, H. - BERSELLI, L. C., On the regularizing effect of the vorticity direction in incompressible viscous flows, Differential Integral Equations, 15 (2002), 345-356. MR1870646
- BEIRÃO DA VEIGA, H. - BERSELLI, L. C., Navier-Stokes equations: Green's matrices, vorticity direction, and regularity up to the boundary, J. Diff. Equations, 246 (2009), 597-628. Zbl1155.35067MR2468730DOI10.1016/j.jde.2008.02.043
- BERSELLI, L. C. - CÓRDOBA, D., On the regularity of the solutions to the 3-D Navier-Stokes equations: a remark on the role of helicity, C.R. Acad. Sci. Paris, Ser.I, 347 (2009), 613-618. MR2532916DOI10.1016/j.crma.2009.03.003
- CONSTANTIN, P. - FEFFERMAN, C., Direction of vorticity and the problem of global regularity for the Navier-Stokes equations, Indiana Univ. Math. J., 42 (1993), 775- 789. Zbl0837.35113MR1254117DOI10.1512/iumj.1993.42.42034
- FOIAŞ, C. - TEMAM, R., Remarques sur les équations de Navier-Stokes stationnaires et les phénomènes successifs de bifurcation. (French), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5 (1978), 28-63. Zbl0384.35047MR481645
- KOZONO, H. - YANAGISAWA, T., variational inequality for vector fields and Helmholtz-Weyl decomposition in bounded domains, Univ. Math. J., 58 (2009), 1853-1920. Zbl1179.35147MR2542982DOI10.1512/iumj.2009.58.3605
- SERRIN, J., Mathematical principles of classical fluid mechanics, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitheraus-geber C. Truesdell), pp. 125-263, Springer-Verlag, Berlin, 1959. MR108116
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