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

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 \(\int_{\mathbb{R}^ 2} u_ 0 (x)dx \neq 0\).

MSC:

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