A new upper bound for the largest growth rate of linear Rayleigh–Taylor instability
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AbstractWe investigate the effect of (interface) surface tensor on the linear Rayleigh–Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold $\vartheta _{\mathrm{c}}$ ϑ c ) by the modified variational method of PDEs. Moreover, we find a new upper bound for Λ. In particular, we directly observe from the upper bound that Λ decreasingly converges to zero as ϑ goes from zero to the threshold $\vartheta _{\mathrm{c}}$ ϑ c .
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1993 ◽
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pp. 363-381
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1995 ◽
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1989 ◽
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2010 ◽
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1895 ◽
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1999 ◽
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1988 ◽
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pp. 301-312
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