2D pressureless gas dynamics and variational principle

Numerical Approximations of Pressureless and Isothermal Gas Dynamics

We study several schemes of rst or second-order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations. The pressureless gas system is weakly hyperbolic, giving rise to the formation of density concentrations known as delta-shocks. For the isothermal gas system, the innnite speed of expansion into vacuum leads to zero timestep in the Godunov method ...

Probabilistic Model Associated with the Pressureless Gas Dynamics

Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we construct a solution to the Riemann problem for the pressureless gas dynamics describing sticky particles. As a bridging step we consider a medium consisting of noninteracting particles. We analyze the difference in the behavior of discontinuous solutions for these two models and t...

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Symbolic Dynamics and the Discrete Variational Principle

We show how to construct symbolic dynamics for the class of 2d-dimensional twist mappings generated by piecewise strictly convex/concave generating functions. The method is constructive and gives an eecient way to nd all periodic orbits of these high dimensional symplectic mappings. It is illustrated with the cardioid and the stadium billiard.

Beyond pressureless gas dynamics : Quadrature-based velocity moment models