Smooth approximation is not a selection principle for the transport equations with rough vector field

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Smooth approximation is not a selection principle for the transport equations with rough vector field

JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)

ID	4614676
Author(s)	Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
Author(s) at UniBasel	Crippa, Gianluca Ciampa, Gennaro
Year	2020
Title	Smooth approximation is not a selection principle for the transport equations with rough vector field
Journal	Calculus of Variations and Partial Differential Equations
Volume	59
Pages / Article-Number	13
Abstract	In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a unique limit, which would be the selected solution of the limit problem. To this aim, we give a new example of a vector field which admits infinitely many flows. Then we construct a smooth approximating sequence of the vector field for which the corresponding solutions have subsequences converging to different solutions of the limit equation.
Publisher	Springer
ISSN/ISBN	0944-2669 ; 1432-0835
edoc-URL	https://edoc.unibas.ch/81397/
Full Text on edoc	Available
Digital Object Identifier DOI	10.1007/s00526-019-1659-0

10/05/2024

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