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The existence of global solutions to a fluid dynamic model for materials for Korteweg type. (English) Zbl 0881.35095

Authors’ abstract: “We discuss the existence of global solutions to a fluid dynamic model for materials of Korteweg type and discuss the three-dimensional nonisothermal motion. The higher-order derivatives of density in the constitutive relation makes it necessary to introduce an interstitial working term in the energy equation. This makes the energy estimate more involved. Nevertheless, it is possible to show the existence of global solutions by the energy method”.
Reviewer: R.Racke (Konstanz)

MSC:

35Q35 PDEs in connection with fluid mechanics
35M10 PDEs of mixed type
76N15 Gas dynamics (general theory)
35K30 Initial value problems for higher-order parabolic equations
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