Ill-posedness of basic equations of fluid dynamics in Besov spaces

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dc.creatorCheskidov, A.
dc.creatorShvydkoy, R.
dc.date2009-04-14
dc.date.accessioned2026-07-07T13:04:08Z
dc.date.available2026-07-07T13:04:08Z
dc.descriptionWe give a construction of a divergence-free vector field $u_0 \in H^s \cap B^{-1}_{\infty,\infty}$, for all $s<1/2$, such that any Leray-Hopf solution to the Navier-Stokes equation starting from $u_0$ is discontinuous at $t=0$ in the metric of $B^{-1}_{\infty,\infty}$. For the Euler equation a similar result is proved in all Besov spaces $B^s_{r,\infty}$ where $s>0$ if $r>2$, and $s>n(2/r-1)$ if $1 \leq r \leq 2$.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0904.2196
dc.identifierhttp://arxiv.org/abs/0904.2196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227054
dc.subjectAnalysis of PDEs
dc.subject76D03; 35Q30
dc.titleIll-posedness of basic equations of fluid dynamics in Besov spaces
dc.typetext

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