The uniqueness of the two-phase incompressible collision jet flows

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This research aims to establish the uniqueness of solutions for two-phase incompressible collision jet flows, specifically addressing the challenges posed by discontinuous velocity at the free boundary.
Used variational methods to build upon previous existence results.
Applied the principle of extremum and moving plane techniques for analysis.
Utilized the Hopf lemma to investigate elliptic equations and free boundary conditions.
Demonstrated that the solutions for two-dimensional two-phase collision jet flows are unique under discontinuous velocity conditions.
Established that the asymptotic direction of the solutions is also uniquely determined.

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Analysis confirms uniqueness of solutions for two-phase collision jet flows with discontinuous velocity.

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He et al. (2026) studied this question.

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