On the supnorm form of Leray's problem for the incompressible Navier-Stokes equations

0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is the Stokes approximation, as well as other fundamental results. In spite of the difficulty of these questions, our approach is elementary and is based on standard tools like conventional Fourier and energy methods.
Comment: We give a simple solution to the asymptotic Leray's problem for the incompressible Navier-Stokes equation based on earlier work by the authors and collaborators. Besides the new results shown here, new proofs to some well known results are also given -->
Druh dokumentu: Working Paper
DOI: 10.1063/1.4923331
Přístupová URL adresa: http://arxiv.org/abs/1807.00197
Přírůstkové číslo: edsarx.1807.00197
Autor: Schutz, Lineia, Zingano, Janaína P., Zingano, Paulo R.
Rok vydání: 2018
Předmět:
Zdroj: Journal of Mathematical Physics, vol. 56, 07 1504 (2015)
Druh dokumentu: Working Paper
DOI: 10.1063/1.4923331
Popis: We show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t) - v(.,t) ||_{sup} --> 0 as t --> infty, where v(.,t) is the Stokes approximation, as well as other fundamental results. In spite of the difficulty of these questions, our approach is elementary and is based on standard tools like conventional Fourier and energy methods.
Comment: We give a simple solution to the asymptotic Leray's problem for the incompressible Navier-Stokes equation based on earlier work by the authors and collaborators. Besides the new results shown here, new proofs to some well known results are also given
Databáze: arXiv
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