The uniqueness of the two-phase incompressible collision jet flows

Key Points

• 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.