115 citations · 1.9k across the 226 of their papers we have counts for
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Global well-posedness of Kirchhoff systems
Tokio Matsuyama, Michael Ruzhansky
The aim of this paper is to establish the global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integratio…
A pseudo-differential calculus on graded Lie groups
Veronique Fischer, Michael Ruzhansky
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of s…
Trace theorems: critical cases and best constants
Michael Ruzhansky, Mitsuru Sugimoto
The purpose of this paper is to present the critical cases of the trace theorems for the restriction of functions to closed surfaces, and to give the asymptotics for the norms of t…
Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
Aparajita Dasgupta, Michael Ruzhansky
In this paper we give global characterisations of Gevrey-Roumieu and Gevrey-Beurling spaces of ultradifferentiable functions on compact Lie groups in terms of the representation th…
Weakly hyperbolic equations with non-analytic coefficients and lower order terms
Claudia Garetto, Michael Ruzhansky
In this paper we consider weakly hyperbolic equations of higher orders in arbitrary dimensions with time-dependent coefficients and lower order terms. We prove the Gevrey well-pose…
Modulation Spaces and Nonlinear Evolution Equations
Michael Ruzhansky, Mitsuru Sugimoto, Baoxiang Wang
We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniqu…