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# Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type

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# Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type

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KOTSCHOTE, Matthias, 2012. Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type. In: SIAM Journal on Mathematical Analysis. 44(1), pp. 74-101. ISSN 0036-1410. eISSN 1095-7154. Available under: doi: 10.1137/110821202

@article{Kotschote2012Dynam-25505, title={Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type}, year={2012}, doi={10.1137/110821202}, number={1}, volume={44}, issn={0036-1410}, journal={SIAM Journal on Mathematical Analysis}, pages={74--101}, author={Kotschote, Matthias} }

Kotschote, Matthias The equations of motion for compressible fluids of Korteweg type as derived by Dunn and Serrin in 1985 are studied in their full generality: the Korteweg tensor is assumed to be an arbitrary function of the form $\mathcal{K} := \left( - \rho^2 \partial_{\rho} \psi + \rho \nabla \cdot ( \kappa \nabla \rho) \right) \mathcal{I} - \kappa \nabla \rho \otimes \nabla \rho, \quad \kappa := 2 \rho \partial_{\phi} \psi(\rho,\theta,\phi), \quad \phi:=|\nabla \rho|^2,$ where $\psi$ denotes Helmholtz free energy density and the capillarity $\kappa$ is subject only to the natural positivity conditions $\kappa(\rho,\theta,\phi) >0, \quad \kappa(\rho,\theta,\phi) + 2 \phi \partial_{\phi} \kappa(\rho,\theta,\phi) > 0, \quad \rho, \theta, \phi \ge 0.$ The viscous stress is supposed to be of generalized Newtonian type. The main result of the paper establishes well-posedness on domains with compact boundaries; the proof is based on refined methods of maximal regularity. 2013-12-18T08:24:32Z SIAM Journal on Mathematical Analysis ; 44 (2012), 1. - S. 74-101 Kotschote, Matthias 2013-12-18T08:24:32Z eng 2012 Dynamics of Compressible Non-isothermal Fluids of Non-Newtonian Korteweg Type terms-of-use