Abstract We give a short proof of local well-posedness for the initial boundary value problem in general relativity with sole condition requirement that is umbilic. This includes as special case totally geodesic we had previously addressed [ 8]. The based on wave coordinates and key observation momentum constraint always valid umbilic boundaries. allows greater freedom choice conditions, since ...

In this paper we consider an initial and boundary value problem modeling the self-propelled motion of solids in a bi-dimensional viscous incompressible uid. The self-propelling mechanism, consisting in appropriate deformations of the solids, is a simpli ed model for the propulsion mechanism of sh-like swimmers. The governing equations are composed of the Navier-Stokes equations for the uid, cou...

Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant ...

We consider the Maxwell-Lorentz equations, i.e., the equation of motion of a charged dust coupled to Maxwell’s equations, on an arbitrary general-relativistic spacetime. We decompose this system of equations into evolution equations and constraints, and we demonstrate that the evolution equations are strongly hyperbolic. This result guarantees that the initial-value problem of the Maxwell-Loren...

We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.

The relativistic Vlasov-Maxwell system of plasma physics is considered with initial data on a past light cone. This characteristic initial value problem arises in a natural way as a mathematical framework to study the existence of solutions isolated from incoming radiation. Conservation laws and a priori estimates of smooth solutions are first derived in a formal way. In the spherically symmetr...