18 citations · 20 across the 13 of their papers we have counts for
13 papers
Complex-valued modified Zakharov Kuznetsov equation
Carlos E. Kenig, Nataša Pavlović, Gigliola Staffilani +1
Motivated by the introduction of the Zakharov-Kuznetsov equation as a higher dimensional generalization of the Korteweg-de Vries equation, in this paper we introduce the modified Z…
Low-regularity invariant measure for the complex-valued mKdV
Zachary Lee, Nataša Pavlović, Gigliola Staffilani +1
In this paper we consider the twice-renormalized, complex-valued modified KdV (mKdV) on the one-dimensional torus introduced by Chapouto. Our main result is the construction of an…
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…
An inverse Problem for the cubic -NLS in Sobolev spaces
Zachary Lee, Nataša Pavlović
In this work, we address an inverse problem for a defocusing cubic nonlinear Schrödinger (NLS) equation in dimensions in a range of Sobolev spaces $H^s(\mathbb{R}^…
Emergence of fermion-mediated interactions in Bose-Fermi mixtures
Esteban Cárdenas, Joseph K. Miller, David Mitrouskas +1
This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an…
Well-posedness and invariant measures for complex valued modified KdV equation
Carlos E. Kenig, Andrea R. Nahmod, Nataša Pavlović +2
We consider the one dimensional periodic complex valued mKdV, which corresponds to the first equation above cubic NLS in the associated integrable hierarchy. Our main result is the…
Derivation of the Higher Order Boltzmann Equation for Hard Spheres
Ioakeim Ampatzoglou, Nataša Pavlović, William Warner
In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas…
On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy
Ioakeim Ampatzoglou, Joseph K. Miller, Nataša Pavlović +1
In this paper we establish the global in time existence and uniqueness of solutions to the Boltzmann hierarchy, a hierarchy of equations instrumental for the rigorous derivation of…
On the effective dynamics of Bose-Fermi mixtures
Esteban Cárdenas, Joseph K. Miller, Nataša Pavlović
In this work, we describe the dynamics of a Bose-Einstein condensate interacting with a degenerate Fermi gas, at zero temperature. First, we analyze the mean-field approximation of…
Derivation of a Boltzmann equation with higher-order collisions from a generalized Kac model
Esteban Cárdenas, Nataša Pavlović, William Warner
In this work, we generalize M. Kac's original many-particle binary stochastic model to derive a space homogeneous Boltzmann equation that includes a linear combination of higher-or…
On an critical Boltzmann equation
Thomas Chen, Ryan Denlinger, Nataša Pavlović
We prove the existence of a class of large global scattering solutions of Boltzmann's equation with constant collision kernel in two dimensions. These solutions are found for …
Ill-posedness of the Navier-Stokes equations in a critical space in 3D
Jean Bourgain, Nataša Pavlović
We prove that the Cauchy problem for the three dimensional Navier-Stokes equations is ill posed in in the sense that a ``norm inflation'' happens in…