Non-Divergence From Operators and Variations on Yau's Explosion Criterion.
In this paper a geometrical link between partial differential equations (PDE) and special coordinate nets on two-dimensional smooth manifolds with the a priori given curvature is suggested. The notion of G-class (the Gauss class) of differential equations admitting such an interpretation is introduced. The perspective of this approach is the possibility of applying the instruments and methods of non-Euclidean geometry to the investigation of differential equations. The equations generated by the...
Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
In this paper, we study the nonexistence of entire positive solution for a conformal -Hessian inequality in via the method of proof by contradiction.
We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on . To prove these results, some new average quantities are...