Related papers: C^\infty smoothing for weak solutions of the inhom…
We consider weak solutions of the spatially inhomogeneous Landau equation with hard potentials ($\gamma \in (0,1]$), under the assumption that mass, energy, and entropy densities are under control. In this regime, with arbitrary initial…
We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under…
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform…
We consider the spatially inhomogeneous Landau equation in the case of very soft and Coulomb potentials, $\gamma \in [-3,-2]$. We show that solutions can be continued as long as the following three quantities remain finite, uniformly in $t$…
We consider the spatially inhomogeneous Landau equation with soft potentials, including the case of Coulomb interactions. First, we establish the existence of solutions for a short time, assuming the initial data is in a fourth-order…
We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish…
This paper deals with the space-homogenous Landau equation with very soft potentials, including the Coulomb case. This nonlinear equation is of parabolic type with diffusion matrix given by the convolution product of the solution with the…
We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main…
In this manuscript we investigate the regularization of solutions for the spatially homogeneous Landau equation. For moderately soft potentials, it is shown that weak solutions become smooth instantaneously and stay so over all times, and…
This paper investigates the Cauchy problem of the spatially homogeneous Landau equation with soft potential under the perturbation framework to global equilibrium. We prove that the solution to the Cauchy problem exhibits analyticity in the…
We consider the spatially inhomogeneous Landau equation with hard potentials (i.e. with $\gamma \in [0,1]$) on the whole space $\mathbb{R}^3$. We prove existence and uniquenss of solutions for a small time, assuming that the initial data is…
This paper deals with some global in time a priori estimates of the spatially homogeneous Landau equation for soft potentials $\ga\in[-2,0)$. For the first result, we obtain the estimate of weak solutions in $L^{\alpha}_{t}L_{v}^{3-\eps}$…
In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy problem enjoys the analytic regularizing effect of the time variable with an L2…
Although the compressible fluid limit of the Boltzmann equation with cutoff has been well investigated in [6] and [13], it still remains largely open to obtain analogous results in case of the angular non-cutoff or even in the grazing limit…
This work deals with the inhomogeneous Landau equation on the torus in the cases of hard, maxwellian and moderately soft potentials. We first investigate the linearized equation and we prove exponential decay estimates for the associated…
This paper addresses large-data local existence and uniqueness of classical solutions to the inhomogeneous Landau equation in the hard potentials case (including Maxwell molecules). Solutions have previously been constructed by Chaturvedi…
This paper deals with the derivation of some \'a priori estimates for the homogeneous Landau equation with soft potentials. Using the coercivity of the Landau operator for soft potentials, we prove a global estimate of weak solutions in…
We study the pointwise (in the space and time variables) behavior of the linearized Landau equation for hard and moderately soft potentials. The solution has very clear description in the $(x,t)-$variables, including large time behavior and…
In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every $L^1$ weak solution to the Cauchy problem with finite moments of all order acquires the $C^\infty$ regularity in the…
In this paper, we study the smoothness effect of Cauchy problem for the spatially homogeneous Landau equation in the hard potential case and the Maxwellian molecules case. We obtain the analytic smoothing effect for the solutions under…