Global strong solutions to the compressible NSK system exist in R^2 and R^3 for arbitrarily large initial data with non-vacuum far-field density.
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On the Cauchy problem for the multi-dimensional compressible Navier-Stokes-Korteweg system: Global strong solutions with arbitrarily large initial data
Global strong solutions to the compressible NSK system exist in R^2 and R^3 for arbitrarily large initial data with non-vacuum far-field density.