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Published in:
The Work of Yoshihiro Shibata Read chapter Read first chapter

2016 | OriginalPaper | Chapter

On Global Well/Ill-Posedness of the Euler-Poisson System

Author : Eduard Feireisl

Published in: Recent Developments of Mathematical Fluid Mechanics

Publisher: Springer Basel

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Abstract

We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of total energy, together with the associated relative entropy inequality. We show that strong solutions are unique in the class of dissipative solutions (weak-strong uniqueness). Finally, we use the method of convex integration to show that the Euler-Poisson system may admit even infinitely many weak dissipative solutions emanating from the same initial data.

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previous chapter Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria
next chapter On the Motion of a Liquid-Filled Rigid Body Subject to a Time-Periodic Torque
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Metadata
Title
On Global Well/Ill-Posedness of the Euler-Poisson System
Author
Eduard Feireisl
Copyright Year
2016
Publisher
Springer Basel
Book
Recent Developments of Mathematical Fluid Mechanics

Print ISBN: 978-3-0348-0938-2

Electronic ISBN: 978-3-0348-0939-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-0348-0939-9_12

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