Resumen de On the ill-posedness of the compressible Navier–Stokes equations in the critical Besov spaces

Qionglei Chen, Changxing Miao, Zhifei Zhang

• We prove the ill-posedness of the 3-D baratropic Navier–Stokes equation for the initial density and velocity belonging to the critical Besov space (B˙3/p,1+ρ¯,B˙3/p−1p,1)(B˙p,13/p+ρ¯,B˙p,13/p−1) for p>6 in the sense that a "norm inflation" happens in finite time, here ρ¯ is a positive constant. While, the compressible viscous heat-conductive flows is ill-posed for the initial density, velocity and temperature belonging to the critical Besov space (B˙3/p,1+ρ¯,B˙3/p−1p,1,B˙3/p−2p,1)(B˙p,13/p+ρ¯,B˙p,13/p−1,B˙p,13/p−2) for p>3.