30 research outputs found

    Global Classical and Weak Solutions to the Three-Dimensional Full Compressible Navier-Stokes System with Vacuum and Large Oscillations

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    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

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    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 λ=ρβ\lambda = \rho^{\beta} with β>4/3\beta>4/3. These results generalize and improve the previous ones due to Vaigant-Kazhikhov([Sib. Math. J. (1995), 36(6), 1283-1316]) which requires β>3\beta>3. 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

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    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
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