Well-Posedness in Smooth Function Spaces for the Moving-Boundary Three-Dimensional Compressible Euler Equations in Physical Vacuum

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Global Existence of Smooth Solutions and Convergence to Barenblatt Solutions for the Physical Vacuum Free Boundary Problem of Compressible Euler Equations with Damping (2014, methodology): “This is one of the new ingredients of the present work compared with the methods used either for the local existence theory in [11, 5, 3, 6, 12] or the nonlinear instability theory in [14].”
Well-posedness of the Muskat problem with H2 initial data (2014, methodology): “Our method can also be applied to the Stefan problem [39], to the free-boundary problem for the incompressible Euler equations [23,26], as well as to the compressible Euler equations [21,25].”
Well‐posedness of Compressible Euler Equations in a Physical Vacuum (2010, methodology): “In particular, the corresponding behavior to h D 1 2 is the case of physical vacuum [10, 12, 13, 31].”