Abstract
In this paper, we investigate the convergence rates of the solution to the incompressible inhomogeneous fluid models of Korteweg type in three-dimensional whole space. We prove that as the capillarity coefficient and viscosity coefficient vanish, the local-in-time solution of the Cauchy problem for this system converges to the solution of the incompressible inhomogeneous Euler equations. In the end, we obtain a continuation theorem for the local smooth solution.
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