相关论文: The $\infty(x)$-equation in Grushin-type Spaces
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
We study the evolution of one-dimensional relativistic jets, using the exact solution of the Riemann problem for relativistic flows. For this purpose, we solve equations for the ideal special relativistic fluid composed of dissimilar…
We establish the stability of metric viscosity solutions to first-order Hamilton--Jacobi equations under Gromov--Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions…
To measure the characteristics of quark and gluon jets in hadron-hadron collisions, two samples of jets are used. Given the large statistics of jets at the LHC, the two-sample method requires taking into account the following corrections:…
We construct a Schwarzschild-type exact external solution for a theory of gravity admitting local Galilean invariance. In order to realize the Galilean invariance we need to adopt a five-dimensional manifold. The solution for the…
Gravitational stability of torsion and inflaton field in a four-dimensional spacetime de Sitter solution in scalar-tensor cosmology where Cartan torsion propagates is investigated in detail. Inflaton and torsion evolution equations are…
In this paper, we consider a class of prescribed Weingarten curvature equations. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the prescribed…
In this expository work, we present Vishik's theorem on non-unique weak solutions to the two-dimensional Euler equations on the whole space, \[ \partial_t \omega + u \cdot \nabla \omega = f \, , \quad u = \frac{1}{2\pi}…
This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the…
We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…
The forced 2D Euler equations exhibit non-unique solutions with vorticity in $L^p$, $p > 1$, whereas the corresponding Navier-Stokes solutions are unique. We investigate whether the inviscid limit $\nu \to 0^+$ from the forced 2D…
Extragalactic relativistic jets are composed by charged particles and magnetic fields, as inferred from the synchrotron emission that we receive from them. The Larmor radii of the particles propagating along the magnetic field are much…
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Enskog equation. Based on a McKean-Vlasov stochastic equation with jumps, the associated…
A new class of solutions which yields an $(n+1)$-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the…
In this paper we construct modified cosmic Chaplygin gas which has viscosity. We use exponential function method to solve non-linear equation and obtain time-dependent dark energy density. Then discuss Hubble expansion parameter and scale…
In this paper, we consider the global existence and uniqueness of the classical solutions for the 3D viscous liquid-gas two-phase flow model. Initial data is only small in the energy-norm. Our main ideas come from [15] where the existence…
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
We consider the Vlasov-Poisson equation in $\mathbb{R}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we…
We study a Grushin critical problem in a strip domain which satisfies the periodic boundary conditions. By applying the finite-dimensional reduction method, we construct a periodic solution when the prescribed curvature function is…