By Gianluca Crippa
The goal of this booklet is to supply a self-contained creation and an updated survey on many points of the speculation of shipping equations and usual differential equations with non-smooth speed fields. The curiosity during this subject is inspired through very important concerns in nonlinear PDEs, particularly conservation legislation and fluid mechanics. a desirable characteristic of this examine region, that's at present of outrage in arithmetic, is the interaction among PDE thoughts and geometric degree idea techniques.
Several masterpieces seem within the comparable literature, balancing thoroughly rigorous proofs with extra heuristic arguments. A constant a part of the publication is predicated on effects got via the writer in collaboration with different mathematicians. After a quick creation to the classical soft idea, the e-book is split into components. the 1st half specializes in the PDE element of the matter, proposing a few common instruments of this research, many well-posedness effects, an summary characterization of the well-posedness, and a few examples displaying the sharpness of the assumptions made. the second one half, in its place, bargains with the ODE element of the matter, respectively via an summary reference to the PDE, and through a few direct and straightforward (but robust) a priori estimates.