ON THE ILL-POSEDNESS OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

By Qionglei Chen, Changxing Miao, Zhifei Zhang. 2011

58 citations recorded by the source corpus.

We prove the ill-posedness of three dimensional compressible viscous heat-conductive flows for the initial data belonging to the critical Besov space ( u B 3 p p,1 + ¯ �, u B 3 p −1 p,1 , u B 3 p −2 p,1 ) for p > 3, here ¯ � is a positive constant. Especially, this result means that it seems impossible to construct a global solution for the highly oscillating initial velocity for the viscous heat-conductive flows. We also prove that the baratropic Navier-Stokes equation is ill-posed for the initial data belonging to the critical Besov space ( u B 3 p p,1 + ¯ �, u B 3 p −1 p,1 ) for p > 6.

Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bf3a1f89fd76804e3f693272f9dd88f3b27fdb56