62 citations · 72 across the 7 of their papers we have counts for
10 papers
Large self-similar solutions of a convection--diffusion equation
Xiaoxin Zheng, Dominika Pilarczyk, Grzegorz Karch +1
We construct self-similar solutions to a nonlinear convection--diffusion equation posed on the whole Euclidean space, for a class of homogeneous initial data. The corresponding sel…
Self-similar solution for fractional Laplacian in cones
Krzysztof Bogdan, Piotr Knosalla, Łukasz Leżaj +1
We construct a self-similar solution of the heat equation for the fractional Laplacian with Dirichlet boundary conditions in every fat cone. As applications, we give the Yaglom lim…
Self-similar solution for Hardy operator
Krzysztof Bogdan, Tomasz Jakubowski, Panki Kim +1
We describe the large-time asymptotics of solutions to the heat equation for the fractional Laplacian with added subcritical or even critical Hardy-type potential. The asymptotics…
Stability of singular solutions to the Navier-Stokes system
Marco Cannone, Grzegorz Karch, Dominika Pilarczyk +1
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three…
Around a singular solution of a nonlocal nonlinear heat equation
Piotr Biler, Dominika Pilarczyk
We study the existence of global-in-time solutions for a nonlinear heat equation with nonlocal diffusion, power nonlinearity and suitably small data (either compared pointwisely to…
Global radial solutions in classical Keller-Segel model of chemotaxis
Piotr Biler, Grzegorz Karch, Dominika Pilarczyk
We consider the simplest parabolic-elliptic model of chemotaxis in the whole space in several dimensions. Criteria for the existence of radial global-in-time solutions in terms of…
Fractional Laplacian with Hardy potential
Krzysztof Bogdan, Tomasz Grzywny, Tomasz Jakubowski +1
We give sharp two-sided estimates of the semigroup generated by the fractional Laplacian plus the Hardy potential on , including the case of the critical constant. We…
-asymptotic stability of mild solutions to Navier-Stokes system in
Grzegorz Karch, Dominika Pilarczyk, Maria E. Schonbek
We consider global-in-time small mild solutions of the initial value problem to the incompressible Navier-Stokes equations in . For such solutions, an asymptotic stability is…
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 stability of singular solution to nonlinear heat equation
Dominika Pilarczyk
In this paper, we discuss the asymptotic stability of singular steady states of the nonlinear heat equation in the weighted Lebesgue norms.