On some properties for an incompressible, non-viscous in-out flow in a 2D domain

Abstract: In this talk I will present some recent results on some properties of an in-out flow associated with a perfect two dimensional fluid. In particular I present existence of solutions in different classes of regularity and I will conclude with the study of the asymptotic limit of some shrinking sources and sinks. This work is motivated by a question left open by Judovic in [2]. The system consists of an Euler type system in a bounded domain with some holes where non-homogeneous boundary conditions are prescribed. I will present how to extend some classical existence results in this setting and then I will consider the case when the holes shrink to points. The boundary conditions lead to the creation of some point sources and sinks associated with some vortex points in the limit. Similar type of systems have been already study by Chemetov and Starovoitov in [1], where a different approximation approach was considered.

References

[1] Chemetov, N. V., Starovoitov, V. N. (2002). On a Motion of a Perfect Fluid in a Domain with Sources and Sinks. Journal of Mathematical Fluid Mechanics, 4(2), 128–144.

[2] Judovic, V. I. (1964). A two-dimensional non-stationary problem on the flow of an ideal incompressible fluid through a given region. (Russian) Mat. Sb. (N.S.) 64 (106) 562–588

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

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