We are concerned with the construction of global smooth large-amplitude solutions to the Cauchy problem of the one-dimensional nonisothermal compressible fluid models of Korteweg type with density- and/or temperature-dependent viscosity, capillarity, and heat conductivity coefficients. Two types of global solvability results are obtained if the viscosity, capillarity, and heat conductivity coefficients satisfy some conditions, and the key point in our analysis is to deduce the positive lower and upper bounds on the density and the temperature.
Zeitschrift für angewandte Mathematik und Physik – Springer Journals
Published: Jun 15, 2017
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