Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows

Abels H, Diening L, Terasawa Y (2014)
Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal 15: 149-157.

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We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak solutions for general initial data and arbitrarily large times with the aid of a parabolic Lipschitz truncation method, which preserves solenoidal velocity fields and was recently developed by Breit, Diening, and Schwarzacher.
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Abels H, Diening L, Terasawa Y. Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal. 2014;15:149-157.
Abels, H., Diening, L., & Terasawa, Y. (2014). Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 15, 149-157. doi:10.1016/j.nonrwa.2013.07.001
Abels, H., Diening, L., and Terasawa, Y. (2014). Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal 15, 149-157.
Abels, H., Diening, L., & Terasawa, Y., 2014. Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 15, p 149-157.
H. Abels, L. Diening, and Y. Terasawa, “Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows”, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 15, 2014, pp. 149-157.
Abels, H., Diening, L., Terasawa, Y.: Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal. 15, 149-157 (2014).
Abels, Helmut, Diening, Lars, and Terasawa, Yutaka. “Existence of weak solutions for a diffuse interface model of non-Newtonian two-phase flows”. Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal 15 (2014): 149-157.
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