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arXiv · 2503.00571

The transition problem between time-independent motions of a body in a viscous liquid

Giovanni P. Galdi·Toshiaki Hishida
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Abstract

A body $\mathscr B$ moves in an unbounded Navier-Stokes liquid by time-independent translatory motion. Suppose that at time $t=0$, $\mathscr B$ smoothly changes its motion to an arbitrary rigid motion, reached at time $t=1$. We then show that the associated Navier-Stokes problem has a unique solution connecting the two steady-states generated by the motion of $\mathscr B$, provided all the involved velocities of $\mathscr B$ are sufficiently small.

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Giovanni P. Galdi, Toshiaki Hishida. 2025-03-01. The transition problem between time-independent motions of a body in a viscous liquid. https://doi.org/10.1007/s00028-026-01194-x

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