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On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity

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  • It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularity in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup phenomena, it remains to give a possible blowup mechanism. In this paper, we present a simple continuation principle for such system, which asserts that the concentration of the density or the temperature occurs in finite time for a large class of smooth initial data, which is responsible for the breakdown of classical solutions. It also gives an affirmative answer to a strong version of a problem proposed by J.Nash in 1950s.
    Mathematics Subject Classification: Primary: 35B65, 35Q35, 76N10.

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