A local asymptotic expansion for a solution of the Stokes system
Güher Çamliyurt, Igor Kukavica · Evolution equations and control theory · 2016
We consider solutions of the Stokes system in a neighborhood of apoint in which the velocity $u$ vanishes of order $d$. We prove that thereexists a divergence-free polynomial $P$ in $x$ with $t$-dependent coefficientsof degree $d$ which approximates the solution $u$ of order $d+\alpha$for certain $\alpha>0$.The polynomial $P$ satisfies a Stokes equation with a forcing term whichis a sum of two polynomials in $x$ of degrees $d-1$ and $d$.