We study the strong solution to the 3-D compressible Navier– Stokes equations. We propose a new blow up criterion for barotropic gases in terms of the integral norm of density ρ and the divergence of the velocity u without any restriction on the physical viscosity constants. Our blow up criteria can be seen as a partial realization of the underlying principle that higher integrability implies boundedness and then eventual regularity. We also present a similar blow-up criterion for heat conducting gases.
|Title of host publication||Contemporary Mathematics|
|Publisher||American Mathematical Society|
|Number of pages||20|
|Publication status||Published - 2018|
Bibliographical noteFunding Information:
H. Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A5A1009350). M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2016R1C1B2015731).
© 2018 American Mathematical Society.
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