Abstract
We first recall results on space-time decay of solutions to the Navier-Stokes equation in the whole space ℝn which were developed in [9] and [1]. Next we give an example of a solution with radial vorticity to the Navier-Stokes equations in 2D, where the space-time decay rate can be computed explicitly.
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References
Amrouche, C., Girault, V., Schonbek, M.E. and Schonbek, T.P. Pointwise decay of solutions and higher derivatives to Navier-Stokes equations. Preprint.
Kajikiya, R. and Miyakawa, T. (1986). On the L2 decay of weak solutions of the Navier-Stokes equations in ℝn. Math. Z., 192:135–148.
Kato, T. (1982). Strong Lp solutions of the Navier-Stokes equations with applications to weak solutions. Math. Z., 187:471–480.
Kozono, H. (1989). Weak and classical solutions of the two-dimensional magneto-hydrodynamic equations. Tohoku Math. J., 41:471–488.
Kozono, H. and Ogawa, T. (1993). Two dimensional Navier-Stokes equations in unbounded domains. Math. Ann., 297:1–31.
Schonbek, M.E. (1985). L2 decay of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal., 88:209–222.
Schonbek, M.E. (1986). Large time behavior of solutions to the Navier-Stokes equations. Comm. Partial Differential Equations, 11:733–763.
Schonbek, M.E. (1991). Lower bounds of rates of decay for solutions to the Navier-Stokes equations. J. Amer. Math. Soc., 4:423–449.
Schonbek, M.E. and Schonbek, T.P. On the boundedness and decay of moments of solutions of the Navier-Stokes equations. Preprint.
Schonbek, M.E., Schonbek, T.P. and Sûli, E. (1996). Large-time behavior of solutions to the Magneto-Hydrodynamic equations. Math. Ann., 304(4):717–756.
Schonbek M.E. and Wiegner, M. (1996). On the decay of higher order norms of the solutions of Navier-Stokes equations. Proceedings of the Royal Society of Edinburgh, section A-Mathematics, 126:677–685.
Takahashi, S. A weighted equation approach to decay rate estimates for the Navier-Stokes equations. Preprint.
Wiegner, M. (1987). Decay results for weak solutions to the Navier-Stokes equations in ℝn. J. London Math. Soc. (2), 35:303–313.
Zhang Linghai. Sharp rates of decay of global solutions to 2-dimensional Navier-Stokes equations. Preprint.
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© 2002 Kluwer Academic Publishers
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Schonbek, M.E. (2002). On Decay of Solustions to the Navier-Stokes Equations. In: Sequeira, A., da Veiga, H.B., Videman, J.H. (eds) Applied Nonlinear Analysis. Springer, Boston, MA. https://doi.org/10.1007/0-306-47096-9_34
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DOI: https://doi.org/10.1007/0-306-47096-9_34
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-46303-7
Online ISBN: 978-0-306-47096-7
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