Sharp rate of decay of solutions to 2-dimensional Navier-Stokes equations. (English) Zbl 0823.35145

Zhang, Linghai

Commun. Partial Differ. Equations 20, No. 1-2, 119-127 (1995).

The author studies the optimal decay rate of global solutions to the initial value problem for the two-dimensional incompressible Navier- Stokes equations \[ u_ t+ u\nabla u- \Delta u+ \nabla p=0, \quad \nabla\cdot u=0, \quad u(x,0)= u_ 0(x), \qquad x\in \mathbb{R}^ 2. \] He proves, using Fourier transform methods, that a solution satisfies the estimate \(\| u(t) \|_{L^ 2}\leq C(1+ t)^{-1/2}\), provided \(u_ 0\in L^ 1\cap H^ 2\) and \(\int_{\mathbb{R}^ 2} u_ 0 (x)dx \neq 0\).

Reviewer: K.Pflüger (Berlin)

MSC:

35Q30	Navier-Stokes equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

optimal decay rate of global solutions; two-dimensional incompressible Navier-Stokes equations; Fourier transform

References:

[1]	DOI: 10.1002/cpa.3160350604 · Zbl 0509.35067
[2]	DOI: 10.1007/BF00752111 · Zbl 0602.76031
[3]	DOI: 10.1080/03605308608820443 · Zbl 0607.35071
[4]	DOI: 10.1112/jlms/s2-35.2.303 · Zbl 0652.35095
[5]	Linghai Zhang, (China) Advances in Math 22 pp 469– (1993)
[6]	Temam, R. 1979. ”Navier-Stokes Equations, Theory and Numerical Analysis”. North-Holland, New York: Amsterdam. · Zbl 0426.35003