The aim of this study is to provide the modeling and exact analytic solutions for hydromagnetic oscillatory rotating flows of an incompressible Burgers’ fluid bounded by a plate. The governing time-dependent equation for the Burgers’ fluid is different than those from the NavierStokes’ equation. The entire system is assumed to rotate around an axis normal to the plate. The governing equations f...

The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503–3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singula...

As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size [4]. In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equati...