Bressan's problem on mixing flows (CROSBI ID 698798)
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Podaci o odgovornosti
Kovač, Vjekoslav
engleski
Bressan's problem on mixing flows
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.
mixing problem
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Podaci o prilogu
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Podaci o skupu
ApplMath18
predavanje
17.09.2018-20.09.2018
Šibenik, Hrvatska