56 citations · 98 across the 31 of their papers we have counts for
35 papers
Finite time singularities in the Landau equation with very hard potentials
Jacob Bedrossian, Jiajie Chen, Maria Pia Gualdani +3
We consider the inhomogeneous Landau equation with and construct smooth, strictly positive initial data that develop a finite time singularity. The -norm o…
Uniqueness for the Homogeneous Landau-Coulomb Equation in
Maria Pia Gualdani, Weiran Sun
We prove the uniqueness of -solutions to the homogeneous Landau-Coulomb equation satisfying and $\langle v \rang…
From the quantum Boltzmann operator to the quantum Landau operator
Maria Pia Gualdani, Nataša Pavlović, Justin Toyota +1
In this manuscript we derive the quantum Landau operator as the weak-coupling limit of the quantum Boltzmann operator (also known as the Uehling-Uhlenbeck operator). We consider bo…
The fuzzy Landau equation: global well-posedness and Fisher information
Maria Pia Gualdani, Nestor Guillen, Nataša Pavlović +2
We investigate a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for a range of soft potentials. The sp…
The -Operator and Uniqueness of Nonlinear Kinetic Equations
Ricardo Alonso, Maria Pia Gualdani, Weiran Sun
We introduce an -operator approach to establish the uniqueness of continuous or bounded solutions for a broad class of Landau-type nonlinear kinetic equations. The spe…
Contractivity of Wasserstein distance and exponential decay for the Landau equation with Maxwellian molecules
F. -U. Caja-Lopez, M. G. Delgadino, M. -P. Gualdani +1
Following the breakthrough work of Guillen and Silvestre \cite{GS24}, that shows that the Fisher information is monotonically decreasing for solutions to the homogeneous Landau equ…
Production of the Fisher information for the Landau-Coulomb equation with L1 initial data
Laurent Desvillettes, William Golding, Maria Pia Gualdani +1
We consider the Landau-Coulomb equation for initial data with bounded mass, finite numbers of moments, and entropy. We show the existence of a global weak solution that has bounded…
A blow-down mechanism for the Landau-Coulomb equation
Maria Pia Gualdani, Raphael Winter
We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian f…
A quasilinear Keller-Segel model with saturated discontinuous advection
Maria Gualdani, Mikel Ispizua, Nicola Zamponi
We consider the singular limit of a chemotaxis model of bacterial collective motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models aggregation-diffusion phe…
Global smooth solutions to the Landau-Coulomb equation in
William Golding, Maria Gualdani, Amélie Loher
We consider the homogeneous Landau equation in with Coulomb potential and initial data in polynomially weighted . We show that there exists a smooth solutio…
Time-Fractional Porous Medium Type Equations. Sharp Time Decay and Regularization
Matteo Bonforte, Maria Gualdani, Peio Ibarrondo
We consider a class of porous medium type of equations with Caputo time derivative. The prototype problem reads as $\Dc u=-\A u^m$ and is posed on a bounded Euclidean domain $Ω\sub…
Regularization estimates of the Landau-Coulomb diffusion
Rene Cabrera, Maria Gualdani, Nestor Guillen
The Landau-Coulomb equation is an important model in plasma physics featuring both nonlinear diffusion and reaction terms. In this manuscript we focus on the diffusion operator wit…
Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium
William Golding, Maria Gualdani, Amélie Loher
We consider the Landau equation with Coulomb potential in the spatially homogeneous case. We show short time propagation of smallness in norms for and instantaneous r…
Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential
William Golding, Maria Pia Gualdani, Nicola Zamponi
In this paper, we prove global-in-time existence and uniqueness of smooth solutions to the homogeneous Landau-Fermi-Dirac equation with Coulomb potential. The initial conditions ar…
Hardy's inequality and (almost) the Landau equation
Maria Gualdani, Nestor Guillen
In this manuscript we establish an estimate for the isotropic analogue of the homogeneous Landau equation. This is done for values of the interaction exponent in (a…
Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations
Jacob Bedrossian, Maria Pia Gualdani, Stanley Snelson
We consider the homogeneous and inhomogeneous Landau equation for very soft and Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not exist unde…
Non-Local Porous Media Equations with Fractional Time Derivative
Esther S. Daus, Maria Pia Gualdani, Jingjing Xu +2
In this paper we investigate existence of solutions for the system: \begin{equation*} \left\{ \begin{array}{l} D^α_tu=\textrm{div}(u \nabla p),\\ D^α_tp=-(-Δ)^{s}p+u^{2}, \end{arra…
Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions
Jann-Long Chern, Maria Gualdani
We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in th…
Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb Potential
François Golse, Maria Pia Gualdani, Cyril Imbert +1
We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal.…
Longtime behavior and weak-strong uniqueness for a nonlocal porous media equation
Esther S. Daus, Maria Gualdani, Nicola Zamponi
In this manuscript we consider a non-local porous medium equation with non-local diffusion effects given by a fractional heat operator \begin{equation*} \partial_t u = \mbox{div}(u…
Existence of weak solutions to a continuity equation with space time nonlocal Darcy law
Luis Caffarelli, Maria Gualdani, Nicola Zamponi
In this manuscript we consider a porous medium equation with non-local diffusion effects given by a fractional heat operator in two space dimensions. Global i…
A review for an isotropic Landau model
Maria Gualdani, Nicola Zamponi
We consider the equation $u_t = \mbox{Div}(a[u]\nabla u - u\nabla a[u])$, . This model has attracted some attention in the recents years and several results are available…
Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential
Maria Gualdani, Nicola Zamponi
In this manuscript we consider an isotropic modification for the Landau equation with Coulomb potential in three space dimensions. Global in time existence of weak solutions for ev…
Spectral gap and exponential convergence to equilibrium for a multi-species Landau system
Maria Gualdani, Nicola Zamponi
In this paper we prove new constructive coercivity estimates and convergence to equilibrium for a spatially non-homogeneous system of Landau equations with soft potentials. We show…