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Exact self-consistent particle-like solutions with spherical and/or cylindrical symmetry to the equations governing the interacting system of scalar, electromagnetic and gravitational fields have been obtained. As a particular case it is…
The search of finite-time singularity solutions of Euler equations is considered for the case of an incompressible and inviscid fluid. Under the assumption that a finite-time blow-up solution may be spatially anisotropic as time goes by…
We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic…
In this paper, we present exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of strings fluid with cosmological constant in $D>4$ dimensions. Both charged and uncharged cases are considered. We focus on the…
We considered the solutions of the Friedmann equation in several setups, arguing that the Weierstra$\ss$ form of the solutions leads to connections with some Conformal Field Theory on a torus. Thus a link with the Cardy entropy formula is…
We analyze the asymptotic properties a special solution of the $(3,4)$ string equation, which appears in the study of the multicritical quartic $2$-matrix model. In particular, we show that in a certain parameter regime, the corresponding…
Extending a previous single-temperature model, an electrostatic gyrofluid model that includes anisotropic temperatures (parallel and perpendicular) and can treat general nonlinear situations is constructed. The model is based on a…
We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and…
We describe the interaction pattern in the $x$-$y$ plane for a family of soliton solutions of the Kadomtsev-Petviashvili (KP) equation, $(-4u_{t}+u_{xxx}+6uu_x)_{x}+3u_{yy}=0$. Those solutions also satisfy the finite Toda lattice hierarchy.…
For the natural initial conditions $L^1$ in the density field (more generally a positive bounded Radon measure) and $L^\infty$ in the velocity field we obtain global approximate solutions to the Cauchy problem for the 3-D systems of…
We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the…
We study the Dirac-Maxwell system coupled with an external potential of Coulomb type. We use the Foldy--Wouthuysen (unitary) transformation of the Dirac operator and its realization as an elliptic problem in the 4-dim half space…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
The perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient which is tangent to the fluid flow (T-models) are studied from a thermodynamic approach. All the admissible…
Three types of blow-up for a fourth-order degenerate reaction-diffusion equation are studied by a combination of analytic and numerical methods. At the critical values of parameters, there occurs a variational problem with a countable set…
We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension…
Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of such a solution provides a tropical approximation to the solution when the variables x,…
We describe a high-order ADER-DG solver for the compressible Euler equations within the ExaHyPE framework. The implementation combines a high-order ADER-DG polynomial representation, a local space-time DG predictor, adaptive mesh…