Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model

  • Robert Lasarzik

    Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
  • Elisabetta Rocca

    Università di Pavia, Italy
  • Giulio Schimperna

    Università di Pavia, Italy
Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model cover

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Abstract

In this paper, we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [25] in two and three dimensions of space. We use a notion of solution inspired by [16], where the pointwise internal energy balance is replaced by the total energy inequality complemented with a weak form of the entropy inequality. Moreover, we prove the existence of local-in-time strong solutions and, finally, we show weak-strong uniqueness of solutions, meaning that every weak solution coincides with a local strong solution emanating from the same initial data, as long as the latter exists.

Cite this article

Robert Lasarzik, Elisabetta Rocca, Giulio Schimperna, Weak solutions and weak-strong uniqueness for a thermodynamically consistent phase-field model. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 2, pp. 229–269

DOI 10.4171/RLM/970