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Weak-Strong Uniqueness and Relaxation Limit for a Navier--Stokes--Korteweg Model
- Speaker(s)
- Nilasis Chaudhuri
- Affiliation
- MIM UW
- Language of the talk
- English
- Date
- April 16, 2026, 12:30 p.m.
- Room
- room 5070
- Seminar
- Seminar of Mathematical Physics Equations Group
In this talk, we study a parabolic relaxation model for a compressible fluid with capillarity effects in an isothermal setting, involving relaxation parameters $\alpha,\beta>0$ that formally drive the system toward the compressible Navier--Stokes--Korteweg equations in the limit $\alpha \to \infty$ and $\beta \to 0$.
We introduce a notion of finite-energy weak solutions for the associated initial--boundary value problem in three spatial dimensions and establish a weak--strong uniqueness principle, ensuring that weak and strong solutions with the same initial data coincide as long as the strong solution exists, for the relaxed system.
Finally, we provide a convergence result in the relaxation limit at the level of finite-energy weak solutions, thereby justifying the model as an approximation of the Navier--Stokes--Korteweg system, even for general non-monotone pressure--density relations.
We introduce a notion of finite-energy weak solutions for the associated initial--boundary value problem in three spatial dimensions and establish a weak--strong uniqueness principle, ensuring that weak and strong solutions with the same initial data coincide as long as the strong solution exists, for the relaxed system.
Finally, we provide a convergence result in the relaxation limit at the level of finite-energy weak solutions, thereby justifying the model as an approximation of the Navier--Stokes--Korteweg system, even for general non-monotone pressure--density relations.
