Large time behaviour of solutions to the 3D-NSE in \mathcal X^σ spaces

2019/01/26 by Jamel Benameur, Benameur, Jamel, Mariem Bennaceur +1
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.09122

Abstract

In this paper we study the incompressible Navier-Stokes equations in L²(\mathbb R³)∩\mathcal X^-1(\mathbb R³). In the global existence case, we establish that if the solution u is in the space C(\mathbb R⁺,L²∩\mathcal X^-1), then for σ>-3/2 the decay of ‖u(t)‖_{\mathcal X^σ} is at least of the order of t^{-(σ+(3)/(2))/(2)}. Fourier analysis and standard techniques are used.

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