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Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations with Applications to the Vlasov-Poisson and Semigeostrophic Systems
Author
Title
Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations [electronic resource] : with Applications to the Vlasov-Poisson and Semigeostrophic Systems / by Maria Colombo.
ISBN
9788876426070
Publication
Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2017.
Physical Description
Approx. 250 p. : online resource.
Local Notes
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Summary
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.
Variant and related titles
Springer ebooks.
Other formats
Printed edition:
Format
Books / Online
Language
English
Added to Catalog
July 06, 2017
Series
Publications of the Scuola Normale Superiore ; 22
Contents
An overview on flows of vector fields and on optimal transport
Maximal regular flows for non-smooth vector fields
Main properties of maximal regular flows and analysis of blow-up
Lagrangian structure of transport equations
The continuity equation with an integrable damping term
Regularity results for very degenerate elliptic equations
An excess-decay result for a class of degenerate elliptic equations
The Vlasov-Poisson system
The semigeostrophic system. .
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