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Decay results for weak solutions of the Navier-Stokes equations on \({\mathbb{R}}\) n. (English) Zbl 0652.35095
The paper deals with the Cauchy problem of the Navier-Stokes equation on R n. The author derives the decay result of \(L_ 2\)-norm of a weak solution u of the above problem. These decay results depend solely on the decay of the solution \(u_ 0\) of the heat problem with the same data. The main tool is the Fourier transform. The existence of a solution for the case \(n\leq 4\) is examined in the appendix.
Reviewer: I.Bock

MSC:
35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations
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