97 citations · 327 across the 42 of their papers we have counts for
46 papers · 1 filter
Comparative Analysis of Obstacle Approximation Strategies for the Steady Incompressible Navier-Stokes Equations
Piotr Krzyżanowski, Sadokat Malikova, Piotr B. Mucha +1
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we inv…
A multifluid model with chemically reacting components -- construction of weak solutions
Piotr B. Mucha, Sarka Necasova, Maja Szlenk
We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation…
A new construction of weak solutions to compressible Navier-Stokes equations
Nilasis Chaudhuri, Piotr B. Mucha, Ewelina Zatorska
We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure for in three space dimension. The…
A fuzzy -closest alignment model
Piotr B. Mucha, Jan Peszek
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the -closest neighbors, known also as the Cucker-Dong mo…
Burgers' equation revisited: extension of mono-dimensional case on a network
Piotr Bogusław Mucha, Aleksandra Puchalska
The paper deals with the analysis of Burgers' equation on acyclic metric graphs. The main goal is to establish the existence of weak solutions in the -- class of regularity. A…
Stability of the density patches problem with vacuum for incompressible inhomogeneous viscous flows
Raphaël Danchin, Piotr B. Mucha, Tomasz Piasecki
We consider the inhomogeneous incompressible Navier-Stokes system in a smooth two or three dimensional bounded domain, in the case where the initial density is only bounded. Existe…
Reacting multi-component fluids -- regular solutions in Lorentz spaces
Piotr B. Mucha, Tomasz Piasecki
The paper deals with analysis of a model of a multi-component fluid admitting chemical reactions. The flow is considered in the incompressible regime. The main result shows global…
Density-induced Consensus Protocol
Piotr Minakowski, Piotr B. Mucha, Jan Peszek
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, d…
Boussinesq system with measure forcing
Piotr B. Mucha, Liutang Xue
We address a question concerning the issue of existence to a Boussinesq type system with a heat source. The problem is studied in the whole two dimensional plane and the heat sourc…
Compressible Navier-Stokes equations with ripped density
Raphaël Danchin, Piotr Boguslaw Mucha
Here we prove the all-time propagation of the Sobolev regularity for the velocity field solution of the two-dimensional compressible Navier-Stokes equations, provided the volume (b…
Singular Cucker-Smale Dynamics
Piotr Minakowski, Piotr B. Mucha, Jan Peszek +1
The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mes…
Regular solutions to the fractional Euler alignment system in the Besov spaces framework
Raphaël Danchin, Piotr B. Mucha, Jan Peszek +1
We here construct (large) local and small global-in-time regular unique solutions to the fractional Euler alignment system in the whole space , in the case where the…
Between homogeneous and inhomogeneous Navier-Stokes systems: the issue of stability
Piotr B. Mucha, Liutang Xue, Xiaoxin Zheng
We construct large velocity vector solutions to the three dimensional inhomogeneous Navier-Stokes system. The result is proved via the stability of two dimensional solutions with c…
From compressible to incompressible inhomogeneous flows in the case of large data
Raphaël Danchin, Piotr Boguslaw Mucha
This paper is concerned with the mathematical derivation of the inhomoge-neous incompressible Navier-Stokes equations (INS) from the compressible Navier-Stokes equations (CNS) in t…
Finite-energy solutions for compressible two-fluid Stokes system
Didier Bresch, Piotr B. Mucha, Ewelina Zatorska
We prove existence of global in time weak solutions to a compressible two-fluid Stokes system with a single velocity field and algebraic closure for the pressure law. The constitut…
The incompressible navier-stokes equations in vacuum
Raphaël Danchin, Piotr Boguslaw Mucha
We are concerned with the existence and uniqueness issue for the inhomogeneous incompressible Navier-Stokes equations supplemented with H^1 initial velocity and only bounded nonneg…
Flocking particles in a non-Newtonian shear thickening fluid
Piotr B. Mucha, Jan Peszek, Milan Pokorny
We prove existence and uniqueness of strong solutions to the Cucker--Smale flocking model coupled with an incompressible viscous non-Newtonian fluid, with the stress tensor of a po…
Total variation denoising in anisotropy
Michał Łasica, Salvador Moll, Piotr B. Mucha
We aim at constructing solutions to the minimizing problem for the variant of Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the gradient flow of its underly…
Steady solutions to viscous shallow water equations. The case of heavy water
Šimon Axmann, Piotr B. Mucha, Milan Pokorný
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as…
Existence of weak solutions for compressible Navier-Stokes equations with entropy transport
David Maltese, Martin Michalek, Piotr B. Mucha +3
We consider the compressible Navier-Stokes system with variable entropy. The pressure is a nonlinear function of the density and the entropy/potential temperature which, unlike in…
Compressible Navier-Stokes system : large solutions and incompressible limit
Raphaël Danchin, Piotr B. Mucha
Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier-Stokes equations supplemented with arbitrary large initial velocity $v\_0…
Stability of high-temperature viscous flows. A case of pudding model
Piotr B. Mucha, Agnieszka Świerczewska-Gwiazda
We investigate the Navier-Stokes-Fourier system for incompressible heat conducting inhomogeneous fluid. The main result concerns existence of global in time regular large solutions…
Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces
Jacek Cyranka, Piotr B Mucha, Edriss S Titi +1
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time extern…
Existence of stationary weak solutions for the heat conducting flows
Piotr B. Mucha, Milan Pokorný, Ewelina Zatorska
The steady compressible Navier--Stokes--Fourier system is considered, with either Dirichlet or Navier boundary conditions for the velocity and the heat flux on the boundary proport…