Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savaré. Their proof uses a discrete particle approximation and stability properties for first-order differential inclusions. Here we give a more direct proof that relies on a result by Haraux on the differentiability of metric projections. We apply the same method also to the one-dimensional Euler-Poisson system, obtaining a new proof for the global existence of weak solutions.

A simple proof of global existence for the 1D pressureless gas dynamics equations / F. Cavalletti, M. Sedjro, M. Westdickenberg. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 47:1(2015), pp. 66-79. [10.1137/130945296]

A simple proof of global existence for the 1D pressureless gas dynamics equations

F. Cavalletti
Primo
;
2015

Abstract

Sticky particle solutions to the one-dimensional pressureless gas dynamics equations can be constructed by a suitable metric projection onto the cone of monotone maps, as was shown in recent work by Natile and Savaré. Their proof uses a discrete particle approximation and stability properties for first-order differential inclusions. Here we give a more direct proof that relies on a result by Haraux on the differentiability of metric projections. We apply the same method also to the one-dimensional Euler-Poisson system, obtaining a new proof for the global existence of weak solutions.
Optimal transport; Pressureles gas dynamics;
Settore MAT/05 - Analisi Matematica
2015
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84924000941&partnerID=40&md5=3967c32f1b832d5c9cadbb32bfb759a5
Article (author)
File in questo prodotto:
File Dimensione Formato  
pressureless.pdf

accesso riservato

Tipologia: Publisher's version/PDF
Dimensione 205.43 kB
Formato Adobe PDF
205.43 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
1311.3108.pdf

accesso aperto

Tipologia: Pre-print (manoscritto inviato all'editore)
Dimensione 229.22 kB
Formato Adobe PDF
229.22 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1011390
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 20
social impact