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Shape optimization in two-dimensional viscous compressible fluids

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Abstract

We present a method for solving the optimal shape problems for profiles surrounded by viscous compressible fluids in two space dimensions. The class of admissible profiles is quite general including the minimal volume condition and a constraint on the thickness of the boundary. The fluid flow is modelled by the Navier-Stokes system for a general viscous barotropic fluid with the pressure satisfying p(ϱ) = aϱlogd(ϱ) for large ϱ. Here d > 1 and a > 0.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Zhong Tan & Ying Hui Zhang

  2. Department of Mathematics, Hu’nan Institute of Science and Technology, Yueyang, 414006, P. R. China

    Ying Hui Zhang

Authors
  1. Zhong Tan
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  2. Ying Hui Zhang
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Correspondence to Ying Hui Zhang.

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Supported by National Natural Science Foundation of China-NSAF (Grant No. 10976026)

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Tan, Z., Zhang, Y.H. Shape optimization in two-dimensional viscous compressible fluids. Acta. Math. Sin.-English Ser. 26, 1793–1806 (2010). https://doi.org/10.1007/s10114-010-7584-y

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  • DOI: https://doi.org/10.1007/s10114-010-7584-y

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