Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, October 12, 2015 - 16:00 to 17:00
Location: 
KIdder 350

Speaker Info

Institution: 
Institute of Mathematics AS Czech Republic
Abstract: 

The dynamics of fluids, i.e. liquids and gases, is an important part of the continuum mechanics. This lecture is devoted to the qualitative analysis of mathematical models of motion of a viscous incompressible fluid around a compact body B, translating and rotating in the fluid with given time-independent translational and angular velocities u and ω. The translation can be considered, without the loss of generality, to be parallel to the x3-axis. We shall study the time-periodic Stokes system and Oseen system in the whole space, in an exterior domain and we will investigate the strong solution, weak solution and very weak solution of the problem in Lq setting with corresponding weight describing the behavior in the large distance [3, 4, 5]. Moreover, we shall discuss the fundamental solution of the Oseen ”rotating” system and the asymptotic decay for the Oseen case and also for nonlinear case [1, 2]. In this part we are starting from the fundamental solution introduced by Guenther and Thomann [7], which is different from approach introduced by Galdi and his col. see e.g. [6]. Finally, we shall discuss the problem of motion of rigid body (which is not prescribed) in viscous fluid and the problem of collisions see [8].

References:

[1] P. Deuring, S. Kračmar, Š. Nečasová, Pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity, J. Differential Equations 255 (2013), no. 7, 1576–1606.

[2] P. Deuring, S. Kračmar and Š. Nečasová, On pointwise decay of linearized stationary incompressible viscous flow around rotating and translating bodies, SIAM J. Math. Anal., 43 (2011), 705–738.

[3] R. Farwig, M. Krbec and Š. Nečasová, A weighted Lq - approach to Oseen flow around a rotating body, Math. Methods Appl. Sci. 31 (2008), 551–574.

[4] R. Farwig, M. Krbec and Š. Nečasová, A weighted Lq - approach to Stokes flow around a rotating body, Ann. Univ. Ferrara - Sez. VII. 54 (2008), 61–84.

[5] S. Kračmar, M. Krbec, Š. Nečasová, P. Penel and K. Schumacher, Very weak solutions to the rotating Stokes, Oseen and Navier-Stokes problems in weighted spaces, Submitted.

[6] G. P. Galdi and M. Kyed, Steady-state Navier-Stokes flows past a rotating body: Leray solutions are physically reasonable, Arch. Rat. Mech. Anal., 200 (2011), 21–58.

[7] E. A. Thomann and R. B. Guenther, The fundamental solution of the linearized Navier-Stokes equations for spinning bodies in three spatial dimensions – time dependent case, J. Math. Fluid Mech., 8 (2006), 77–98.

[8] E. Feireisl, M. Hillairet, Š. Nečasová. On the motion of several rigid bodies in an incompressible non-Newtonian fluid. Nonlinearity, 21, 1349–1366, 2008.