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Ernesto Nungesser

Publications and source records attributed to Ernesto Nungesser.

At least 19 recordsLinked to original sources
arXiv2026

The massless Boltzmann equation in Minkowski spacetime

We study the spatially homogeneous, massless Boltzmann equation in Minkowski spacetime for a certain range of hard and soft interactions. For hard interactions, we derive a Povzner-type inequality for massless particles and show that solutions exist for all time into the future. For soft interactions, we employ singular weights to control singularities at $ p = 0 $, which arise from the masslessness of particles, to obtain local existence. These results, which are among rather few proofs of existence for the massless Boltzmann equation, are motivated by our earlier work on the massless Einstein--Boltzmann system in certain cosmological settings.

math.AP↗
arXiv2025

Homogeneous solutions to the Einstein-matter equations with a magnetic field and a conformal gauge singularity

We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are no solutions in the case that the matter model is a radiation fluid. If the matter is described via kinetic theory we obtain that there exist unique solutions to the Einstein-Vlasov system and the Einstein-Boltzmann system for a certain range of soft potentials. For both the Vlasov and the Boltzmann case we also obtain asymptotic expansions close to the initial conformal gauge singularity.

gr-qc↗
arXiv2024

Well-posedness of anisotropic and homogeneous solutions to the Einstein-Boltzmann system with a conformal-gauge singularity

We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and show that the initial value problem is well posed with data given at the singularity. This is understood by considering conformally rescaled equations. The Einstein equations become a system of singular ordinary differential equations, for which we establish an existence theorem which requires several differentiability and eigenvalue conditions on the coefficient functions together with the Fuchsian conditions. The Boltzmann equation is regularized by a suitable choice of time coordinate, but still has singularities in momentum variables. This is resolved by considering singular weights, and the existence is obtained by exploiting singular moment estimates.

gr-qc↗
arXiv2024

Future global existence of homogeneous solutions to the Einstein-Boltzmann system with soft potentials

We study the Cauchy problem for the Einstein-Boltzmann system with soft potentials in a cosmological setting. We assume the Bianchi I symmetry to describe a spatially homogeneous, but anisotropic universe and consider a cosmological constant $ Λ> 0 $ to describe an accelerated expansion of the universe. For the Boltzmann equation we introduce a new weight function and apply the method of Illner and Shinbrot to obtain the future global existence of spatially homogeneous, small solutions. For the Einstein equations we assume that the initial value of the Hubble variable is close to $ ( Λ/ 3 )^{ 1 / 2 } $. We obtain the future global existence and asymptotic behavior of spatially homogeneous solutions to the Einstein-Boltzmann system with soft potentials.

gr-qc↗
arXiv2024

Future of Bianchi I magnetic cosmologies with kinetic matter

We show under the assumption of small data that solutions to the Einstein-Vlasov system with a pure magnetic field and Bianchi I symmetry isotropise and tend to dust solutions. We also obtain the decay rates for the main variables. This generalises part of the work [V.~G.~LeBlanc, Classical Quantum Gravity 14, 2281-2301 (1997)] concerning the future behaviour of orthogonal perfect fluids with a linear equation of state in the presence of a magnetic field to the Vlasov case.

gr-qc↗
arXiv2022

Small solutions of the Einstein-Boltzmann-scalar field system with Bianchi symmetry

We show that small homogeneous solutions to the Einstein-Boltzmann-scalar field system exist globally towards the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I--VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [19], where a cosmological constant was considered, and a generalization of [16], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein-Boltzmann-scalar field system for small initial data.

gr-qc↗
arXiv2022

On almost Ehlers-Geren-Sachs theorems

We show assuming small data that massless solutions to the reflection symmetric Einstein-Vlasov system with Bianchi VII$_0$ symmetry which are not locally rotational symmetric, can be arbitrarily close to and will remain close to isotropy as regards {to} the shear. However in general the shear will not tend to zero and the Hubble normalised Weyl curvature will blow up. This generalises the work \cite{NHW,WHU}, which considered a non-tilted radiation fluid to the massless Vlasov case. This represents another example of the fact that almost Ehlers-Geren-Sachs theorems do not hold in general and that collisionless matter behaves differently than a perfect fluid.

gr-qc↗
arXiv2017

Late-time behaviour of the Einstein-Boltzmann system with a positive cosmological constant

In this paper we study the Einstein-Boltzmann system for Israel particles with a positive cosmological constant. We consider spatially homogeneous solutions of Bianchi types except IX and obtain future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system. The result shows that the solutions converge to the de Sitter solution at late times.

gr-qc↗
arXiv2017

Bianchi I solutions of the Einstein-Boltzmann system with a positive cosmological constant

In this paper we study the future global existence and late-time behaviour of the Einstein-Boltzmann system with Bianchi I symmetry and a positive cosmological constant $Λ>0$. For the Boltzmann equation we consider the scattering kernel of Israel particles which are the relativistic counterpart of Maxwellian particles. Under a smallness assumption on initial data in a suitable norm we show that solutions exist globally in time and isotropize at late times.

math-ph↗
arXiv2017

Self-similarity breaking of cosmological solutions with collisionless matter

In this paper we consider the Einstein-Vlasov system with Bianchi VII$_0$ symmetry. Under the assumption of small data we show that self-similarity breaking occurs for reflection symmetric solutions. This generalizes the previous work concerning the non-tilted fluid case \cite{WHU} to the Vlasov case, and we obtain detailed information about the late-time behaviour of metric and matter terms.

gr-qc↗
arXiv2016

Late-time behaviour of Israel particles in a FLRW spacetime with $Λ>0$

In this paper we study the relativistic Boltzmann equation in a spatially flat FLRW spacetime. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the asymptotic behaviour of solutions. The main argument of the paper is to use the energy method of Guo, and we observe that the method can be applied to study small solutions in a cosmological case. It is the first result of this type where a physically well-motivated scattering kernel is considered for the general relativistic Boltzmann equation.

math-ph↗
arXiv2016

Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry

In this paper we study the Einstein-Boltzmann system with Bianchi I symmetry. Isotropization of Bianchi I spacetimes was proved in [13] in the Vlasov case, and asymptotic behaviour of the relativistic Boltzmann equation was studied in [9] in the isotropic case. These results are generalized in the present paper to the non-isotropic and Boltzmann case. We assume that the initial data are small in a suitable sense, and show that solutions of the Einstein-Boltzmann system are future geodesically complete, that they isotropize and have a dust-like behaviour at late times. Detailed information about the metric and the matter terms is obtained. In short, the solution is asymptotically the Einstein-de Sitter solution.

gr-qc↗
arXiv2014

Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant

We show future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a positive cosmological constant. Estimates of higher derivatives of the metric and the matter terms are obtained using an inductive argument. In a recent research monograph Ringström shows future non-linear stability of (not necessarily symmetric) solutions of the Einstein-Vlasov system with a non-linear scalar field if certain local estimates on the geometry and the matter terms are fulfilled. We show that these assumptions are satisfied at late times for the case under consideration here which together with Cauchy stability leads to our main conclusion.

math-ph↗
arXiv2014

Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein-Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein-Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.

gr-qc↗
arXiv2013

The electromagnetic spike solutions

The aim of this paper is to use the existing relation between polarized electromagnetic Gowdy spacetimes and vacuum Gowdy spacetimes to find explicit solutions for electromagnetic spikes by a procedure which has been developed by one of the authors for gravitational spikes. We present new inhomogeneous solutions which we call the EME and MEM electromagnetic spike solutions.

gr-qc↗
arXiv2012

Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$

In a recent paper arXiv:1208.4231 we have treated the future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI$_0$. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.

gr-qc↗