STICKY PARTICLES AND SCALAR

Niveau: Secondaire, Lycée
STICKY PARTICLES AND SCALAR CONSERVATION LAWS Yann Brenier and Emmanuel Grenier Abstra t One dimensional s alar onservation laws with nonde reasing initial on- ditions and general uxes are shown to be the appropriate equations to des ribe large systems of free parti les on the real line, whi h sti k under ollision with onservation of mass and momentum. Introdu tion There has been a re ent interest for the one dimensional model of pressure- less gases with sti ky parti les. This model an be des ribed at a dis rete level by a nite olle tion of parti les that get stu k together right after they ollide with onservation of mass and momentum. At a ontinuous level, the gas an be des ribed by a density and a velo ity elds (t; x), u(t; x) that satisfy the mass and momentum onservation laws t + x (u) = 0; (1) t u+ x (u 2 ) = 0: (2) This system an be formally obtained from the usual Euler equations for ideal ompressible uids by letting the pressure go to zero, or from the Boltzmann equation by letting the temperature go to zero. This model of adhesion dynami s is onne ted to the sti ky parti le model of Zeldovi h [18?,[16?, whi h also in ludes gravitational intera tions and has interesting statisti al properties.

• entropy solution


• onservation laws


• weight


• when sho ks


• reasing initial


• ontinuous model


• there exists