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pro vyhledávání: '"PITCHO, JULES"'
Autor:
Pitcho, Jules
We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the vector field constructed by Depauw in [Depauw, C. R. Math. Acad. Sci. Pa
Externí odkaz:
http://arxiv.org/abs/2407.02364
Autor:
Pitcho, Jules
The purpose of this work is to demonstrate that the lack of selection by smooth regularisation for the continuity equation with a bounded, divergence-free vector field as demonstrated in \cite{DeLellis_Giri22} by De Lellis and Giri takes place over a
Externí odkaz:
http://arxiv.org/abs/2404.19687
Autor:
Pitcho, Jules
Publikováno v:
J. Evol. Equ. 24, 69 (2024)
We prove that for bounded, divergence-free vector fields in $L^1_{loc}((0,+\infty);BV_{loc}(R^d;R^d))$, regularisation by convolution of the vector field selects a single solution of the transport equation for any integrable initial datum. We recall
Externí odkaz:
http://arxiv.org/abs/2312.17085
Akademický článek
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Autor:
PITCHO, JULES, SORELLA, MASSIMO
Publikováno v:
SIAM Journal on Mathematical Analysis; 2023, Vol. 55 Issue 5, p4640-4663, 24p
Autor:
Pitcho, Jules, Sorella, Massimo
We construct divergence-free Sobolev vector fields in C([0,1];W^{1,r}(T^d;R^d)) with r < d and d >=2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. We then show that the vector fields we produc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ec018625380b4818fdd845dccd26884
https://hal.archives-ouvertes.fr/hal-03363163
https://hal.archives-ouvertes.fr/hal-03363163