62 citations · 62 across the 4 of their papers we have counts for
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Tools for stability analysis of fractional reaction diffusion systems
Sofwah Ahmad, Szymon Cygan, Grzegorz Karch
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of sol…
Solutions at vacuum and rarefaction waves in pressureless Euler alignment system
Szymon Cygan, Grzegorz Karch
We construct global-in-time weak solutions to the pressureless Euler alignment system posed on the whole line and supplemented with initial conditions, where an initial density is…
Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field
Lorenzo Brandolese, Grzegorz Karch
The Navier-Stokes system for an incompressible fluid coupled with the equation for a heat transfer is considered in the whole three dimensional space. This system is invariant unde…
Asymptotic stability of Landau solutions to Navier-Stokes system
Grzegorz Karch, Dominika Pilarczyk
It is known that the three dimensional Navier-Stokes system for an incompressible fluid in the whole space has a one parameter family of explicit stationary solutions, which are ax…
Asymptotic profiles of solutions to convection-diffusion equations
Said Benachour, Grzegorz Karch, Philippe Laurençot
The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that…