arXiv subjects

Lotfi Jlali

Publications and source records attributed to Lotfi Jlali.

4 recordsLinked to original sources

arXiv2023

Higher order evolution inequalities with Hardy potential in the exterior of a half-ball

We consider semilinear higher order (in time) evolution inequalities posed in an exterior domain of the half-space $\mathbb{R}_+^N$, $N\geq 2$, and involving differential operators of the form $\mathcal{L}_λ=-Δ+λ/|x|^2$, where $λ\geq -N^2/4$. A potential function of the form $|x|^τ$, $τ\in \mathbb{R}$, is allowed in front of the power nonlinearity. Under inhomogeneous Dirichlet-type boundary conditions, we show that the dividing line with respect to existence or nonexistence is given by a Fujita-type critical exponent that depends on $λ, N$ and $τ$, but independent of the order of the time derivative.

math.AP↗

arXiv2015

Long time decay for 3D-NSE in Gevrey-Sobolev spaces

In this paper we prove, if $u$ is a global solution to Navier-Stokes equations in the Sobolev-Gevrey spaces $H^1_{a,σ}(\mathbb R^3)$, then $\|u(t)\|_{H^1_{a,σ}}$ decays to zero as time goes to infinity. Fourier analysis is used.

math.AP↗

arXiv2015

Long time decay of 3D-NSE in Lei-Lin-Gevrey spaces

In this paper, we prove that there exists a unique global solution of $3D$ Navier-Stokes equation if $\exp(a|D|^{1/σ})u^0\in{\mathcal{X}}^{-1}(\mathbb R^3)$ and $\|u^0\|_{\mathcal{X}^{-1}}<ν$. Moreover, we will show that $\|\exp(a|D|^{1/σ}) u(t)\|_{\mathcal{X}^{-1}}$ goes to zero if the time $t$ goes to infinity.

math.AP↗

arXiv2015

On the blow up criterion of 3D-NSE in Sobolev-Gevrey spaces

In \cite{JB1}, Benameur proved a blow-up result of the non regular solution of $(NSE)$ in the Sobolev-Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev-Gevrey spaces with less regularity on the initial condition. Fourier analysis is used.

math.AP↗