Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations
With Applications to the Vlasov-Poisson and Semigeostrophic Systems
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Beschreibung
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Provides a mathematical tool to describe the motion of large-scale oceanic/atmospheric flow Focuses on interactions between transport equations and PDEs The Theses was defended at Scuola Normale Superiore, Pisa
Autor*in
Maria Colombo
Themen in »Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations«
Lagrangian flows transport equations Vlasov-Poisson system renormalized solutions degenerate elliptic equation traffic model optimal transportation semigeostrophic equations partial differential equations