Naslov
Bressan's problem on mixing flows

Autori
Kovač, Vjekoslav

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
ApplMath18

Mjesto i datum
Šibenik, Hrvatska, 17.09.2018. - 20.09.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
mixing problem

Sažetak
Around 2003 Alberto Bressan proposed an open problem on two incompressible fluids in a periodic container. Informally saying, it is conjectured that the minimal cost of mixing of the two fluids up to scale $\varepsilon$ grows like $\log(1/\varepsilon)$ as $\varepsilon\to0$. The most natural quantity representing this cost is the total variation of the time-dependent vector field $v$ that causes the mixing. A weaker result, when the $\textup{; ; L}; ; ^1$ norm of $\nabla v$ is replaced by its $\textup{; ; L}; ; ^p$ norm for $p>1$, has been addressed several times in the existing literature. It was first established by Crippa and De Lellis (2006) by reducing it to certain estimates for the maximal function, and a similar technique was employed by Seis (2013). On the other hand, Had\v{; ; z}; ; i\'{; ; c}; ; , Seeger, Smart, and Street (2016) approached the $\textup{; ; L}; ; ^p$ variant of the problem via estimates for multilinear singular integrals, and a modification of their idea was also used by L\'{; ; e}; ; ger (2016). In this talk we discuss yet another approach to the aforementioned problem and its special cases using techniques from harmonic analysis.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA