Estimates on Weighted $L^q$-Norms of the Nonstationary 3D Navier-Stokes Flow in an Exterior Domain (Journal of Partial Differential Equations, 2025)
This paper is devoted to estimates on weighted $L^q$-norms of the nonstationary 3D Navier-Stokes flow in an exterior domain. By multiplying the Navier-Stokes equation with a well selected vector field, an integral equation is derived, from which, we establish the weighted estimate $∥|x|^αu(t)∥_q ≤ C(1+t^{\frac{α}{2} +ε} )t^{-\frac{3}{2}(1-\frac{1}{q})} ,$$t>0,$ where $ 00$ and $1
Keywords: weighted estimates; navier-stokes flow; exterior domain; $L^1$-data.