High-capillarity limit and smoothing effect of large solutions for a multi-dimensional generic non-conservative compressible two-fluid model

Abstract

Abstract We investigate the global existence and long-time behaviour of large solutions in the high-capillarity regime for a general multidimensional non-conservative compressible two-fluid model with the capillary pressure relation f ( α − ρ − ) = P + − P − . Our main contributions are threefold. First, we prove the existence and uniqueness of global solutions in critical Besov spaces for large initial perturbations, under the sharp stability condition − s − 2 ( 1 , 1 ) α − ( 1 , 1 ) < f ′ ( 1 ) < 0 . In particular, we remove the extra negativity condition imposed by Evje et al (2016 Arch. Ration. Mech. Anal. 221 1285–1316). Second, as the capillarity coefficient approaches infinity, we provide a rigorous justification for the global-in-time convergence to the incompressible Navier–Stokes flows and obtain explicit convergence rates in critical spaces for ill-prepared data. Third, if the initial perturbation further belongs to a lower-regularity Besov space, we derive optimal decay rates for the solution and all its derivatives. A crucial novelty of our analysis lies in the refined energy and error estimates that capture the coupling between the parabolic and dispersive mechanisms, thereby removing the smallness condition and revealing the intrinsic parabolic regularization. To the best of our knowledge, this provides the first global well-posedness theory for multidimensional compressible two-fluid flows with large amplitudes.