Global existence of classical solutions to two‐dimensional Navier–Stokes equations with Cauchy data containing vacuum |
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Authors: | Zhen Luo |
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Institution: | 1. School of Mathematical Sciences, Xiamen University, , Xiamen, Fujian 361005, China;2. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, , Shatin, Hong Kong |
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Abstract: | In this paper, the Cauchy problem to the two‐dimensional isentropic compressible Navier–Stokes equations with smooth initial data containing vacuum is investigated. If the initial data are of small energy but possibly large oscillations, we obtain the global well‐posedness of classical solutions in the case of initially nonvacuum far fields. In particular, the smallness of the energy only depends on the norm of the initial velocity, where β can be arbitrary close to 0. In the case of compactly supported initial density, a blow‐up example is given. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | viscous compressible Navier– Stokes Cauchy problem global solution classical solution |
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