arXiv subjects

Youssef Bettaibi

Publications and source records attributed to Youssef Bettaibi.

3 recordsLinked to original sources

arXiv2021

$\mathrm{L}^{2}_α $-Solutions for Nonlinear Schrödinger Equations Associated With The Weinstein Operator

In this paper, we study the Schrödinger equation associated with the Weinstein operators and we prove the existence and uniqueness of global solutions to Schrödinger-Weinstein equations in\\ $C\left(\left(-T_{\min }, T_{\max }\right) ; L_α^{2}\left(\mathbb{R}^{d+1}_+\right)\right) \bigcap L_{l o c}^{q_{1}}\left(\left(-T_{\min }, T_{\max }\right) ; L_α^{r_{1}}\left(\mathbb{R}^{d+1}_+\right)\right)$ \\ on initial condition in $L_α^{2}\left(\mathbb{R}^{d+1}_+\right)$

math.AP↗

arXiv2021

On the Blow-up criterion of Navier-Stokes equation associated with the Weinstein operator

In this paper we give Navier-Stokes system associated with the Weinstein operator $(NSW)$ (see Eq.\eqref{11}), We study the existence and uniqueness of solutions to equations (NSW) in $L_α^{p}\left(\mathbb{R}_{+}^{d+1}\right), 2 α+d+2<p \leq \infty$, and we proved some properties of the maximal solution of equation. If the maximum time $T^*$is finite, we establish that the growth of $\left\| u ( {t}) \right\|_{L ^ {p}_α} $ is at least of the order of ${\left(T^{*}-t\right)^{{-\frac{2 p}{p-2 α-d-2}}}},$ fo rall $t$ in $\left[0, T^{*}\right]$, also we give some blow-up results.

math.AP↗

arXiv2020

Real Paley-Wiener Theorem for the Generalized Weinstein transform in quantum calculus

We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{α, q, a}^{2}$-functions whose q-Weinstein transform has compact support as a subspace of the space of $L_{α, q, a}^{2}$-functions.

math.FA↗