Related papers: Formation of singularity for the rotating shallow …
Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations.…
We study a gravitating spherically symmetric nonrelativistic configuration consisting of a spinor fluid whose effective equation of state is derived from a consideration of a limiting system supported by a massive nonlinear spinor field.…
A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that…
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…
We prove that singularities propagate globally for viscosity solutions of Hamilton-Jacobi equations related to magnetic mechanical systems on closed Riemannian manifolds. Our main result shows that for any weak KAM solution $u$, the…
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
We study a dissipative nonlinear equation modelling certain features of the Navier-Stokes equations. We prove that the evolution of radially symmetric compactly supported initial data does not lead to singularities in dimensions $n\leq 4$.…
We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not…
We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
In this paper, using the similarity method, we construct particular solutions with singularities for degenerate high-order equations. The considered equations have singularities of the first and second kind. Particular solutions are…
Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which…
In this paper we investigate the existence of singular solutions to the conformal Dirac-Einstein system. Because of its conformal invariance, there are many similarities with the classical construction of singular solutions for the Yamabe…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
A second mapping method is introduced in the generalized discrete singular convolution algorithm. The mapping approaches are adopted to regularize singularities for one electron system. The applications of the two mapping methods are…
A theorem, giving necessary and sufficient condition for naked singularity formation in spherically symmetric non static spacetimes under hypotheses of physical acceptability, is formulated and proved. The theorem relates existence of…
We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar field capturing the melt fraction by volume, has been studied…
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the very weak solution with the classical one in some appropriate…
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…
In this paper, we consider radial symmetry property of positive solutions of an integral equation arising from some higher order semi-linear elliptic equations on the whole space $\mathbf{R}^n$. We do not use the usual way to get symmetric…