7 papers · 1 filter
Complex-valued modified Zakharov Kuznetsov equation
Carlos E. Kenig, NataÅ¡a PavloviÄ, 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, NataÅ¡a PavloviÄ, 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, NataÅ¡a PavloviÄ, 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, NataÅ¡a PavloviÄ +2
We study a fuzzy variant of the inhomogeneous Landau equation and establish global-in-time existence and uniqueness of smooth solutions for moderately soft potentials. The spatial…
An inverse Problem for the cubic -NLS in Sobolev spaces
Zachary Lee, NataÅ¡a PavloviÄ
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}…
Well-posedness and invariant measures for complex valued modified KdV equation
Carlos E. Kenig, Andrea R. Nahmod, NataÅ¡a PavloviÄ +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…