On questions of decay and existence for the viscous Camassa–Holm equations
Clayton Bjorland; Maria E. Schonbek
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 5, page 907-936
- ISSN: 0294-1449
Access Full Article
topHow to cite
topBjorland, Clayton, and Schonbek, Maria E.. "On questions of decay and existence for the viscous Camassa–Holm equations." Annales de l'I.H.P. Analyse non linéaire 25.5 (2008): 907-936. <http://eudml.org/doc/78819>.
@article{Bjorland2008,
author = {Bjorland, Clayton, Schonbek, Maria E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {regularity; decay without a rate; algebraic rate},
language = {eng},
number = {5},
pages = {907-936},
publisher = {Elsevier},
title = {On questions of decay and existence for the viscous Camassa–Holm equations},
url = {http://eudml.org/doc/78819},
volume = {25},
year = {2008},
}
TY - JOUR
AU - Bjorland, Clayton
AU - Schonbek, Maria E.
TI - On questions of decay and existence for the viscous Camassa–Holm equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2008
PB - Elsevier
VL - 25
IS - 5
SP - 907
EP - 936
LA - eng
KW - regularity; decay without a rate; algebraic rate
UR - http://eudml.org/doc/78819
ER -
References
top- [1] Ben-Artzi M., Global solutions of two-dimensional Navier–Stokes and Euler equations, Arch. Rational Mech. Anal.128 (4) (1994) 329-358. Zbl0837.35110MR1308857
- [2] Caffarelli L., Kohn R., Nirenberg L., Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math.35 (6) (1982) 771-831. Zbl0509.35067MR673830
- [3] Camassa R., Holm D.D., An integrable shallow water equation with peaked solitons, Phys. Rev. Lett.71 (11) (1993) 1661-1664. Zbl0972.35521MR1234453
- [4] Chen S., Foias C., Holm D.D., Olson E., Titi E.S., Wynne S., Camassa–Holm equations as a closure model for turbulent channel and pipe flow, Phys. Rev. Lett.81 (24) (1998) 5338-5341. Zbl1042.76525MR1745983
- [5] Chen S., Foias C., Holm D.D., Olson E., Titi E.S., Wynne S., The Camassa–Holm equations and turbulence, Phys. D133 (1–4) (1999) 49-65. Zbl1194.76069MR1721139
- [6] Chen S., Foias C., Holm D.D., Olson E., Titi E.S., Wynne S., A connection between the Camassa–Holm equations and turbulent flows in channels and pipes, Phys. Fluids11 (8) (1999) 2343-2353. Zbl1147.76357MR1719962
- [7] Constantin P., Foias C., Navier–Stokes Equations, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1988. Zbl0687.35071MR972259
- [8] J.A. Domaradzki, D.D. Holm, Navier–Stokes-alpha model: Les equations with nonlinear dispersion, 2001.
- [9] Foias C., Holm D.D., Titi E.S., The Navier–Stokes-alpha model of fluid turbulence, Phys. D152/153 (2001) 505-519. Zbl1037.76022MR1837927
- [10] Foias C., Holm D.D., Titi E.S., The three dimensional viscous Camassa–Holm equations, and their relation to the Navier–Stokes equations and turbulence theory, J. Dynam. Differential Equations14 (1) (2002) 1-35. Zbl0995.35051MR1878243
- [11] Holm D.D., Marsden J.E., Ratiu T.S., The Euler–Poincaré equations and semidirect products with applications to continuum theories, Adv. Math.137 (1) (1998) 1-81. Zbl0951.37020MR1627802
- [12] Holm D.D., Titi E.S., Computational models of turbulence: The lans-α model and the role of global analysis, SIAM News38 (2005).
- [13] Hopf E., Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr.4 (1951) 213-231. Zbl0042.10604MR50423
- [14] Ilyin A.A., Titi E.S., Attractors for the two-dimensional Navier–Stokes-α model: an α-dependence study, J. Dynam. Differential Equations15 (4) (2003) 751-778. Zbl1039.35078MR2031580
- [15] Leray J., Essai sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math.63 (1934) 193-248. MR1555394JFM60.0726.05
- [16] Marsden J.E., Shkoller S., Global well-posedness for the Lagrangian averaged Navier–Stokes (LANS-α) equations on bounded domains, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci.359 (1784) (2001) 1449-1468. Zbl1006.35074MR1853633
- [17] Masuda K., Weak solutions of Navier–Stokes equations, Tohoku Math. J. (2)36 (4) (1984) 623-646. Zbl0568.35077MR767409
- [18] Ogawa T., Rajopadhye S.V., Schonbek M.E., Energy decay for a weak solution of the Navier–Stokes equation with slowly varying external forces, J. Funct. Anal.144 (2) (1997) 325-358. Zbl0873.35064MR1432588
- [19] Prodi G., Teoremi di tipo locale per il sistema di Navier–Stokes e stabilità delle soluzioni stazionarie, Rend. Sem. Mat. Univ. Padova32 (1962) 374-397. Zbl0108.28602MR189354
- [20] Schonbek M., The Fourier splitting method, in: Advances in Geometric Analysis and Continuum Mechanics, Stanford, CA, 1993, Internat. Press, Cambridge, MA, 1995, pp. 269-274. Zbl0842.35142MR1356749
- [21] Schonbek M.E., Decay of solutions to parabolic conservation laws, Comm. Partial Differential Equations5 (5) (1980) 449-473. Zbl0476.35012MR571048
- [22] Schonbek M.E., Sharp rate of decay of solutions to 2-dimensional Navier–Stokes equations, Comm. Partial Differential Equations7 (1) (1980) 449-473. Zbl0476.35012
- [23] Schonbek M.E., decay for weak solutions of the Navier–Stokes equations, Arch. Rational Mech. Anal.88 (3) (1985) 209-222. Zbl0602.76031MR775190
- [24] Schonbek M.E., Large time behaviour of solutions to the Navier–Stokes equations, Comm. Partial Differential Equations11 (7) (1986) 733-763. Zbl0607.35071MR837929
- [25] Schonbek M.E., Large time behaviour of solutions to the Navier–Stokes equations in spaces, Comm. Partial Differential Equations20 (1–2) (1995) 103-117. Zbl0831.35132
- [26] Schonbek M.E., Schonbek T.P., Moments and lower bounds in the far-field of solutions to quasi-geostrophic flows, Discrete Contin. Dyn. Syst.13 (5) (2005) 1277-1304. Zbl1091.35070
- [27] Schonbek M.E., Wiegner M., On the decay of higher-order norms of the solutions of Navier–Stokes equations, Proc. Roy. Soc. Edinburgh Sect. A126 (3) (1996) 677-685. Zbl0862.35086
- [28] Temam R., Navier–Stokes Equations. Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, RI, 2001, Reprint of the 1984 edition. Zbl0981.35001
- [29] Wiegner M., Decay results for weak solutions of the Navier–Stokes equations on , J. London Math. Soc. (2)35 (2) (1987) 303-313. Zbl0652.35095
- [30] Wiegner M., Higher order estimates in further dimensions for the solutions of Navier–Stokes equations, in: Evolution Equations, Warsaw, 2001, Banach Center Publ., vol. 60, Polish Acad. Sci., Warsaw, 2003, pp. 81-84. Zbl1029.35198MR1993060
- [31] Zhang L.H., Sharp rate of decay of solutions to 2-dimensional Navier–Stokes equations, Comm. Partial Differential Equations20 (1–2) (1995) 119-127. Zbl0823.35145MR1312702
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.