Wilberclay G. Melo, Nata F. Rocha, Natielle dos Santos Costa
Abstract:
In this article, we prove the existence of a unique global solution for the
critical case of the generalized Navier-Stokes equations in Lei-Lin and
Lei-Lin-Gevrey spaces, by assuming that the initial data is small enough.
Moreover, we obtain a unique local solution for the subcritical case of this
system, for any initial data, in these same spaces. It is important to point
out that our main result is obtained by discussing some properties of the
solutions for the heat equation with fractional dissipation.
Submitted April 18, 2023. Published November 10, 2023.
Math Subject Classifications: 35A01, 35Q35, 42B37.
Key Words: Navier-Stokes equations; global and local solutions; Lei-Lin-Gevrey spaces.
DOI: 10.58997/ejde.2023.78
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Wilberclay G. Melo Departamento de Matemática Universidade Federal de Sergipe São Cristóvão, SE 49100-000, Brazil email: wilberclay@academico.ufs.br |
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Natã F. Rocha Campus Clóvis Moura Universidade Estadual do Piauí Teresina, PI 64078-213, Brazil email: natafirmino@ccm.uespi.br |
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Natielle dos Santos Costa Departamento de Matemática Universidade Federal de Sergipe São Cristóvão, SE 49100-000, Brazil email: natielle.scosta@academico.ufs.br |
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