Diffusion wave terms in the 2D compressible NSK system show different L2 asymptotic decays for density versus potential momentum flow when initial data is in the Hardy space.
Time decay estimate with diffusion wave property and smoothing effect for solutions to the compressible Navier-Stokes-Korteweg system
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abstract
Time decay estimate of solutions to the compressible Navier-Stokes-Korteweg system is studied. Concerning the linearized problem, the decay estimate with diffusion wave property for an initial data is derived. As an application, the time decay estimate of solutions to the nonlinear problem is given. In contrast to the compressible Navier-Stokes system, for linear system regularities of the initial data are lower and independent of the order of derivative of solutions owing to smoothing effect from the Korteweg tensor. Furthermore, for the nonlinear system diffusion wave property is obtained with an initial data having lower regularity than that of study of the compressible Navier-Stokes system.
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2019 1verdicts
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Asymptotic profile for diffusion wave terms of the compressible Navier-Stokes-Korteweg system
Diffusion wave terms in the 2D compressible NSK system show different L2 asymptotic decays for density versus potential momentum flow when initial data is in the Hardy space.