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Global smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with variable viscosity

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Abstract

Under the assumptions that the initial density ρ 0 is close enough to 1 and ρ 0 − 1 ∈ H s+1(ℝ2), u 0 ∈ H s(ℝ2) ∩ Ḣ−ε(ℝ2) for s > 2 and 0 < ε < 1, the authors prove the global existence and uniqueness of smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with the viscous coefficient depending on the density of the fluid. Furthermore, the L 2 decay rate of the velocity field is obtained.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Guilong Gui & Ping Zhang

Authors
  1. Guilong Gui
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  2. Ping Zhang
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Correspondence to Guilong Gui.

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Dedicated to Professor Andrew Majda on the Occasion of his 60th Birthday

Project supported by the National Natural Science Foundation of China (Nos. 10525101, 10421101), the 973 project of the Ministry of Science and Technology of China and the innovation grant from Chinese Academy of Sciences.

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Gui, G., Zhang, P. Global smooth solutions to the 2-D inhomogeneous Navier-Stokes equations with variable viscosity. Chin. Ann. Math. Ser. B 30, 607–630 (2009). https://doi.org/10.1007/s11401-009-0027-3

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  • DOI: https://doi.org/10.1007/s11401-009-0027-3

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