30 research outputs found
Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations
We establish the global existence and uniqueness of classical solutions to
the three-dimensional full compressible Navier-Stokes system with smooth
initial data which are of small energy but possibly large oscillations where
the initial density is allowed to vanish. Moreover, for the initial data which
may be discontinuous and contain vacuum states, we also obtain the global
existence of weak solutions. These results generalize previous ones on
classical and weak solutions for initial density being strictly away from
vacuum, and are the first for global classical and weak solutions which may
have large oscillations and can contain vacuum states.Comment: 61 page
Existence and Blowup Behavior of Global Strong Solutions to the Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
For periodic initial data with initial density allowed to vanish, we
establish the global existence of strong and weak solutions for the
two-dimensional compressible Navier-Stokes equations with no restrictions on
the size of initial data provided the bulk viscosity coefficient is with . These results generalize and improve the
previous ones due to Vaigant-Kazhikhov([Sib. Math. J. (1995), 36(6),
1283-1316]) which requires . Moreover, both the uniform upper bound of
the density and the large-time behavior of the strong and weak solutions are
also obtained.Comment: 31 page
Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations
We establish the global existence and uniqueness of classical solutions to
the Cauchy problem for the isentropic compressible Navier-Stokes equations in
three spatial dimensions with smooth initial data which are of small energy but
possibly large oscillations with constant state as far field which could be
either vacuum or non-vacuum. The initial density is allowed to vanish and the
spatial measure of the set of vacuum can be arbitrarily large, in particular,
the initial density can even have compact support. These results generalize
previous results on classical solutions for initial densities being strictly
away from vacuum, and are the first for global classical solutions which may
have large oscillations and can contain vacuum states.Comment: 30 page