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Asymptotic behaviour of solutions to the Navier-Stokes equations of a two-dimensional compressible flow

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Abstract

In this paper, we are concerned with the asymptotic behaviour of a weak solution to the Navier-Stokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(ϱ) = αϱlogd(ϱ) for large ϱ. Here d > 2, a > 0. We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is also briefly discussed.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, 414006, China

    Ying-hui Zhang

  2. School of Mathematical Sciences, Xiamen University, Fujian, 361005, China

    Zhong Tan

Authors
  1. Ying-hui Zhang
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  2. Zhong Tan
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Correspondence to Ying-hui Zhang.

Additional information

Supported by the National Natural Science Foundation of China (No. 10976026) and Hunan Provincial Natural Science Foundation of China (No. 10JJ6013).

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Zhang, Yh., Tan, Z. Asymptotic behaviour of solutions to the Navier-Stokes equations of a two-dimensional compressible flow. Acta Math. Appl. Sin. Engl. Ser. 27, 697–712 (2011). https://doi.org/10.1007/s10255-011-0115-5

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  • DOI: https://doi.org/10.1007/s10255-011-0115-5

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