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- W2973873982 abstract "Abstract We study the nonlinear Rayleigh–Taylor (RT) instability of an inhomogeneous incompressible viscoelastic fluid in a bounded domain. It is well known that there exist strong solutions of RT instability in $H^{2}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -norm in inhomogeneous incompressible viscoelastic fluids, when the elasticity coefficient κ is less than some threshold $kappa _{mathrm{C}}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:math> . In this paper, we prove the existence of classical solutions of RT instability in $L^{1}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -norm in Lagrangian coordinates based on a bootstrap instability method with finer analysis, if $kappa <kappa _{mathrm{C}}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>κ</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mi>κ</mml:mi> <mml:mi>C</mml:mi> </mml:msub> </mml:math> . Moreover, we also get classical solutions of RT instability in $L^{1}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -norm in Eulerian coordinates by further applying an inverse transformation of Lagrangian coordinates." @default.
- W2973873982 created "2019-09-26" @default.
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- W2973873982 date "2019-09-18" @default.
- W2973873982 modified "2023-10-16" @default.
- W2973873982 title "On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids" @default.
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- W2973873982 doi "https://doi.org/10.1186/s13661-019-1263-4" @default.
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