Abstract
We are concerned with the Cahn–Hilliard/Navier–Stokes equations for the stationary compressible flows in a three-dimensional bounded domain. The governing equations consist of the stationary Navier–Stokes equations describing the compressible fluid flows and the stationary Cahn–Hilliard-type diffuse equation for the mass concentration difference. We prove the existence of weak solutions when the adiabatic exponent \(\gamma \) satisfies \(\gamma >\frac{4}{3}\). The proof is based on the weighted total energy estimates and the new techniques developed to overcome the difficulties from the capillary stress.
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Acknowledgements
The research of Z. Liang was supported by the fundamental research funds for central universities (JBK 2202045). The research of D. Wang was partially supported by the National Science Foundation under grant DMS-1907519. The authors would like to thank the anonymous referees for valuable comments and suggestions.
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Liang, Z., Wang, D. Weak Solutions to the Stationary Cahn–Hilliard/Navier–Stokes Equations for Compressible Fluids. J Nonlinear Sci 32, 41 (2022). https://doi.org/10.1007/s00332-022-09799-5
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DOI: https://doi.org/10.1007/s00332-022-09799-5