currently, cosmetic surgery is spread around the world. several factors are involved in this rapidly evolving field such as socio-economic development, changes in cultural norms, globalization and the effects of western culture, advertising, media, and mental disorders. nowadays the cosmetic surgery is becoming a profitable business, which deals exclusively with human appearance and less from t...

We investigate the solution of an N-unit series system with finite number of vacations. By using CC00-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

Article history: Received 31 August 2015 Available online 27 February 2016 MSC: 35B34 35B35 35B40 35J05 78A25

We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space Hs,a(R), which is defined by the norm ‖φ‖Hs,a = ‖〈ξ〉s−a|ξ|a b φ‖L2 ξ . We obtain the local well-posedness in Hs,a with s ≥ max{−3/4,−a − 3/2}, −3/2 < a ≤ 0 and (s, a) 6= (−3/4,−3/4). The proof is based on Kishimoto’s work [12] which proved the sharp well-posedness in the Sobolev space H−3/4(R...

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We prove the global well-posedness of the viscous incompressible Boussinesq equations in two spatial dimensions for general initial data in Hm with m ≥ 3. It is known that when both the velocity and the density equations have finite positive viscosity, the Boussinesq system does not develop finite time singularities. We consider here the challenging case when viscosity enters only in the veloci...

This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension.

In this paper we prove the global well-posedness for the three-dimensional EulerBoussinesq system with axisymmetric initial data without swirl. This system couples the Euler equation with a transport-diffusion equation governing the temperature.