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Time decay rates of the \(L^3\)-norm for strong solutions to the Navier-Stokes equations in \(\mathbb{R}^3\). (English) Zbl 1435.35059
Summary: Let \(u \in C([0, \infty); L^3(\mathbb{R}^3))\) be a strong solution of the Cauchy problem for the 3D Navier-Stokes equations with the initial value \(u_0\). We prove that the time decay rates of \(u\) in the \(L^3\)-norm coincide with ones of the heat equation with the initial value \(| u_0 |\). Our proofs use the theory about the existence of local strong solutions, time decay rates of strong solutions when the initial value is small enough, and uniqueness arguments.
MSC:
35B40 Asymptotic behavior of solutions to PDEs
35Q30 Navier-Stokes equations
35D35 Strong solutions to PDEs
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