24 citations · 134 across the 80 of their papers we have counts for
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Some Fractional Functional Inequalities and Applications to Some Constrained Minimization Problems Involving a Local Non-linearity
Hichem Hajaiej
In this paper we prove the Fractional Gagliardo-Nirenberg Inequality, Polya-Szego Inequality and the Sharp Fractional Sobolev Inequality, we then provide an application of such ine…
On the Nonlinear Schrodinger systems with local and nonlocal nolinearities Part1
Hichem Hajaiej
We study well-posedness, local and global, existence of solutions for a general class of physically meaningful nonlinear Schrödinger systems with magnetic field involving local and…
On Schrödinger Systems with Local and Nonlocal Nonlinearities - Part II
Hichem Hajaiej
In this second part, we establish the existence of special solutions of the nonlinear Schrödinger system studied in the first part when the diamagnetic field is nul. We also prove…
Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations
Hichem Hajaiej, Luc Molinet, Tohru Ozawa +1
Sufficient and necessary conditions for the generalized Gagliardo-Nirenberg (GN) inequality in Besov spaces and Triebel-Lizorkin spaces are obtained. Applying the GN inequality, we…
On the necessity of the assumptions used to prove Hardy-Littlewood and Riesz Rearrangement Inequalities 1
Hichem Hajaiej
We prove that supermodularity is a necessary condition for the generalized Hardy- Littlewood and Riesz rearrangement inequalities. We also show the necessity of the monotonicity of…
Symmetric Ground States Solutions of M-Coupled Nonlinear Schrodinger Equations
Hichem Hajaiej
We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity.