## 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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