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In this talk, we first revisit the existence theory of weak
solutions for the compressible Navier–Stokes system—one developed by
P.L. Lions and E. Feireisl, and another by D. Bresch and P.E. Jabin. We
propose an approximation scheme that, instead of using the classical
regularization of the continuity equation based on viscosity
approximation, employs a more direct truncation and regularization of
the nonlinear terms and pressure. This scheme is compatible with the
Kolmogorov compactness criterion for the density. |