slideshow 3

Seminar on partial differential equations

Spectral instability of a steady flow of an incompressible viscous fluid past a rotating obstacle

Jiří Neustupa
Institute of Mathematics, Czech Academy of Sciences

 

Tuesday, 15. May 2018 - 9:00 to 10:00

in IM, rear building, ground floor

We show that a steady solution U to the system of equations of motion of an incompressible Newtonian fluid past a rotating body is unstable if an associated linear operator L has at least one eigenvalue in the right half-plane in C. Our theorem does not directly follow from a series of preceding results on instability, mainly because the associated nonlinear operator is not bounded in the same space in which the instability is studied. As an important auxiliary result, we also show that the uniform growth bound of the C_0 semigroup e^{Lt} is equal to the spectral bound of operator L.