LOSS OF SMOOTHNESS AND ENERGY CONSERVING ROUGH WEAK SOLUTIONS FOR THE 3d EULER EQUATIONS

To conclude the proof of Theorem 3.1, we use some monotonicity and one-dimensional symmetry results [3, 10] for positive solutions with bounded gradient of semilinear elliptic

The regularity criterion of the weak solution to the 3D viscous Boussinesq equations in Besov spaces. Fuyi Xu, Qian Zhang, and

They are entirely devoted to the initial value problem and the long-time behavior of solutions for the two-dimensional incompressible Navier–Stokes equations, in the particular

When considering all the profiles having the same horizontal scale (1 here), the point is therefore to choose the smallest vertical scale (2 n here) and to write the decomposition

For regularized MHD equations, Yu and Li [19] studied Gevrey class regularity of the strong solu- tions to the MHD-Leray-alpha equations and Zhao and Li [22] studied analyticity of

The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method

(2010) [2] we show that, in the case of periodic boundary conditions and for arbitrary space dimension d 2, there exist infinitely many global weak solutions to the

As we have mentioned, the purpose of this paper is to perform suitable modifications on the parabolic De-Giorgi’s method developed in [5], so that, after our modifications, the