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<p>A body <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathscr {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> </math></EquationSource> </InlineEquation> moves in an unbounded Navier–Stokes liquid by time-independent translatory motion. Suppose that at time <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(t=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathscr {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> </math></EquationSource> </InlineEquation> smoothly changes its motion to an <i>arbitrary</i> rigid motion, reached at time <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(t=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We then show that the associated Navier–Stokes problem has a unique solution connecting the two steady states generated by the motion of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\mathscr {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> </math></EquationSource> </InlineEquation>, provided all the involved velocities of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({\mathscr {B}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">B</mi> </math></EquationSource> </InlineEquation> are sufficiently small.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月2日

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  • Giovanni P. Galdi,
  • Toshiaki Hishida

摘要

A body \({\mathscr {B}}\) B moves in an unbounded Navier–Stokes liquid by time-independent translatory motion. Suppose that at time \(t=0\) t = 0 , \({\mathscr {B}}\) B smoothly changes its motion to an arbitrary rigid motion, reached at time \(t=1\) 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 \({\mathscr {B}}\) B , provided all the involved velocities of \({\mathscr {B}}\) B are sufficiently small.