No abstract

We consider the Cauchy problem of fractional pseudo-parabolic equation on the whole space R n , n ≥ 1. Here, the fractional order α is related to the diffusion-type source term behaving as the usual diffusion term on the high frequency part. It has a feature of regularity-gain and regularity-loss for α > 1 and 0 < α < 1, respectively. We establish the global existence and time-decay rates for small-amplitude solutions to the Cauchy problem for α > 0. In the case that 0 < α < 1 , we introduce the time-weighted energy method to overcome the weakly dissipative property of the equation.

No abstract

No abstract

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981–3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio γ. Then we prove the blow‐up of smooth solution of compressible Navier–Stokes equations in half space with Navier‐slip boundary. The main ideal is constructing the differential inequality. Copyright © 2017 John Wiley & Sons, Ltd.

No abstract

A class of periodic initial value problems for two-dimensional NewtonBoussinesq equations are investigated in this paper. The Newton-Boussinesq equations are turned into the equivalent integral equations. With iteration methods, the local existence of the solutions is obtained. Using the method of a priori estimates, the global existence of the solution is proved.

No abstract