arXiv subjects
Publications and source records attributed to Mongi Blel.
We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with the nonlinear exponential damping term $a (e^{b |u|^{\bf 2}}-1)u$, ($a,b>0$) studied by the second author in \cite{J1}.
In \cite{CJ}, the authors show that the Cauchy problem of the Navier-Stokes equations with damping $α|u|^{β-1}u(α>0,\;β\geq1)$ has global weak solutions in $L^2(\R^3)$. In this paper, we prove the uniqueness, the continuity in $L^2$ for $β>3$, also the large time decay is proved for $β\geq\frac{10}3$. Fourier analysis and standard techniques are used.
We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).