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Motivation, analysis and control of the variable density Navier-Stokes equations

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  • The main objective of these Notes is to provide an introduction to variable density NS: their motivation, some of the main mathematical problems connected with them, the main techniques used to solve these problems, the main results and open questions. First, we will describe the physical origin of the equations. Then, we will be concerned with existence, uniqueness, regularity and control of initial-boundary value problems in cylindrical domains $ Ω $ $\times (0,T)$; as usual, $ Ω $ is the spatial domain, an open set in $\mathbb{R}$2 or $\mathbb{R}$3 ``filled'' by the fluid particles and (0,T) is the time observation interval. Some open problems (not all them of the same difficulty) are also recalled.
    Mathematics Subject Classification: Primary: 35Q30, 76D05; Secondary: 49J20, 76D55, 93B05.


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