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Mouhamad Medhat El Safadi

Associate professor
Mathematics department - Section III - Tripoli
Speciality: Mathematics
Specific Speciality: Mathématiques

Teaching 6 Taught Courses
Publications 3 publications
R.Alexandre and M. El Safadi Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations II. Non cutoff case and non Maxwellian molecules 2009

We use Littlewood-Paley theory for the analysis of regularization properties of weak solutions of the homogeneous Boltzmann equation. For non cutoff and non Maxwellian molecules, we show that such solutions are smoother than the initial data. In particular, our method applies to any weak solution, though we assume that it belongs to a weighted [L^2] space.

Mouhamad El Safadi Smoothness of weak solutions of the spatially homogeneous Landau equation 2007

We prove that any weak solution to the Landau homogeneous equation is smooth and, in particular, that it lies in Schwartz space . Our result has to be compared to [6], where Desvillettes and Villani have shown existence of smooth weak solutions along with a uniqueness result, under further assumptions on initial data. Our method of proof uses the Littlewood–Paley decomposition of velocity space, and elementary Cauchy–Schwarz or Young's inequalities, thus avoiding any use of complex Sobolev interpolation inequalities.

R.Alexandre and M. El Safadi Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations I. Non cutoff case and Maxwellian molecules 2005

We use Littlewood–Paley theory for the analysis of regularization properties of solutions of the homogeneous Boltzmann equation. For non-cutoff Maxwellian molecules, we show that such solutions are smoother than the initial data. Although the recent and up to date results of Desvillettes and Wennberg assume much more general assumptions on the collision cross sections, our method seems to be simpler than those used earlier to show such properties and also applies to any weak solution.

Languages
English

Professional working proficiency

French

Professional working proficiency