  Consider two compressible immiscible fluids in 1D in the isentropic
approximation. The first fluid is surrounded and in contact with the second
one. As the Mach number of the first fluid vanishes, the coupled dynamics of
the two fluids results as the compressible to incompressible limit and is known
to satisfy an ODE--PDE system. Below, a characterization of this limit is
provided, ensuring its uniqueness.
