On the (x,t) asymptotic properties of solutions of the Navier-Stokes equations in the half-space

被引：0

作者：

Crispo F. ^{[1
]}

Maremonti P. ^{[1
]}

机构：

[1] Dipartimento di Matematica, Seconda Università degli Studi di Napoli

来源：

Journal of Mathematical Sciences | 2006年 / 136卷 / 2期

关键词：

Initial Data; Asymptotic Behavior; Classical Solution; Asymptotic Property; Space Variable;

D O I：

10.1007/s10958-006-0197-4

中图分类号：

学科分类号：

摘要：

We study the space-time asymptotic behavior of classical solutions of the initial-boundary value problem for the Navier-Stokes system in the half-space. We construct a (local in time) solution corresponding to an initial data that is only assumed to be continuous and decreasing at infinity as |x| -μ, μ ∈(1/2,n). We prove pointwise estimates in the space variable. Moreover, if μ ∈[1, n) and the initial data is suitably small, then the above solutions are global (in time), and we prove space-time pointwise estimates. Bibliography: 19 titles. © 2006 Springer Science+Business Media, Inc.

引用

页码：3735 / 3767

页数：32

共 19 条

[1] Fabes E.B., Jones B.F., Riviere N.M., The initial value problem for the Navier-Stokes equations with data in Lp, Arch. Rational Mech. Anal., 45, pp. 222-240, (1972)
[2] Galdi G.P., Sohr H., Existence and Uniqueness of Time-periodic Physically Reasonable Navier-Stokes Flow Past A Body
[3] Giga Y., Inui K., Matsui Sh., On the Cauchy problem for the Navier-Stokes equations with nondecaying initial data, Quad. Mat., 4, pp. 27-68, (1999)
[4] Knightly G.H., On a class of global solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 21, pp. 211-245, (1966)
[5] Knightly G.H., A Cauchy problem for the Navier-Stokes equations in ℝn, SIAM J. Math. Anal., 3, pp. 506-511, (1972)
[6] Knightly G.H., Some decay properties of solutions of the Navier-Stokes equations, Lect. Notes Math., 771, pp. 287-298, (1980)
[7] Koch H., Solonnikov V.A., Lp-Estimates of the first-order derivatives of solutions of the nonstationary Navier-Stokes equations, Nonlinear Problems of Mathematical Physics and Related Topics. I, in Honor of Professor O. A. Ladyzhenskaya, pp. 203-218, (2002)
[8] Ladyzhenskaya O.A., Uraltseva N.N., Linear and Quasi-linear Equations of Elliptic Type, (1968)
[9] Ladyzhenskaya O.A., Solonnikov V.A., Uraltseva N.N., Linear and Quasi-linear Equations of Parabolic Type, 23, (1968)
[10] Maremonti P., Starita G., On the nonstationary Stokes equations in a half-space with continuous initial data, Zap. Nauchn. Semin. POMI, 295, pp. 118-167, (2003)

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