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<p>The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes (CHNS) equations. In this work, we study the well-posedness results for the CHNS system with nonhomogeneous boundary conditions for the velocity equation. We obtain the existence of global weak solutions in the two-dimensional bounded domain. We further prove the continuous dependence of the solution on the initial conditions and boundary data, thereby establishing the uniqueness of the weak solution. The existence of strong solutions is also established in this work.</p>

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On the Cahn-Hilliard-Navier-Stokes equations with nonhomogeneous boundary

  • 期刊论文

  • 发表日期：

    2026年7月14日

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  • Manika Bag,
  • Tania Biswas,
  • Sheetal Dharmatti

摘要

The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes (CHNS) equations. In this work, we study the well-posedness results for the CHNS system with nonhomogeneous boundary conditions for the velocity equation. We obtain the existence of global weak solutions in the two-dimensional bounded domain. We further prove the continuous dependence of the solution on the initial conditions and boundary data, thereby establishing the uniqueness of the weak solution. The existence of strong solutions is also established in this work.