96 citations · 217 across the 23 of their papers we have counts for
35 papers · 1 filter
decay estimates and inviscid limits for Global smooth solutions to the compressible Navier-Stokes-Riesz system
Agnieszka Świerczewska-Gwiazda, Yuan Xu, Junhao Zhang
We study the Cauchy problem in for the repulsive compressible Navier-Stokes-Riesz system with Riesz exponent and viscosity , where the…
On a system of equations arising in meteorology: Well-posedness and data assimilation
Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses…
Unconditional stability of radially symmetric steady sates of compressible viscous fluids with inflow/outflow boundary conditions
Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
We show that certain radially symmetric steady states of compressible viscous fluids in domains with inflow/outflow boundary conditions are unconditionally stable. This means that…
From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit
Charles Elbar, Piotr Gwiazda, Jakub Skrzeczkowski +1
Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation a…
Cahn-Hillard and Keller-Segel systems as high-friction limits of Euler-Korteweg and Euler-Poisson equations
Dennis Gallenmüller, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
We consider a combined system of Euler--Korteweg and Euler--Poisson equations with friction and exponential pressure with exponent . We show the existence of dissipative meas…
Mathematical theory of compressible magnetohydrodynamics driven by non-conservative boundary conditions
Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon +1
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solva…
Time periodic motion of temperature driven compressible fluids
Eduard Feireisl, Piotr Gwiazda, Agnieszka Swierczewska-Gwiazda
We consider the Navier-Stokes-Fourier system describing the motion of a compressible viscous fluid in a container with impermeable boundary subject to time periodic heating and und…
The Rayleigh Benard problem for compressible fluid flows
Eduard Feireisl, Agnieszka Swierczewska-Gwiazda
We consider the physically relevant fully compressible setting of the Rayleigh Benard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected…
Dissipative measure-valued solutions to the Euler-Poisson equation
José A. Carrillo, Tomasz Dębiec, Piotr Gwiazda +1
We consider several pressureless variants of the compressible Euler equation driven by nonlocal repulsionattraction and alignment forces with Poisson interaction. Under an energy a…
Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fract…
A two species hyperbolic-parabolic model of tissue growth
Piotr Gwiazda, Benoît Perthame, Agnieszka Świerczewska-Gwiazda
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a…
On the Extension of Onsager's Conjecture for General Conservation Laws
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +2
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "…
Differentiability in perturbation parameter of measure solutions to perturbed transport equation
Piotr Gwiazda, Sander C. Hille, Kamila Łyczek +1
We consider a linear perturbation in the velocity field of the transport equation. We investigate solutions in the space of bounded Radon measures and show that they are differenti…
Existence and homogenization of nonlinear elliptic systems in nonreflexive spaces
Miroslav Bulíček, Piotr Gwiazda, Martin Kalousek +1
We consider a strongly nonlinear elliptic problem with the homogeneous Dirichlet boundary condition. The growth and the coercivity of the elliptic operator is assumed to be indicat…
Dissipative measure valued solutions for general conservation laws
Piotr Gwiazda, Ondřej Kreml, Agnieszka Świerczewska-Gwiazda
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued -- strong uniqueness principle. T…
Conservation of energy for the Euler-Korteweg equations
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…
Relative entropy method for measure-valued solutions in natural sciences
Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek +1
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the n…
A tribute to conservation of energy for weak solutions
Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolu…
Existence of global weak solutions to the kinetic Peterlin model
Piotr Gwiazda, Mária Lukáčová-Medviďová, Hana Mizerová +1
We consider a class of kinetic models for polymeric fluids motivated by the Peterlin dumbbell theories for dilute polymer solutions with a nonlinear spring law for an infinitely ex…
A note on weak solutions of conservation laws and energy/entropy conservation
Piotr Gwiazda, Martin Michálek, Agnieszka Świerczewska-Gwiazda
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second l…
Homogenization of nonlinear elliptic systems in nonreflexive Musielak-Orlicz spaces
Miroslav Bulíček, Piotr Gwiazda, Martin Kalousek +1
We study the homogenization process for families of strongly nonlinear elliptic systems with the homogeneous Dirichlet boundary conditions. The growth and the coercivity of the ell…
Thermo-visco-elasticity for Norton-Hoff-type models with homogeneous thermal expansion
Piotr Gwiazda, Filip Z. Klawe, Sebastian Owczarek
In this work we study a quasi-static evolution of thermo-visco-elastic model with homogeneous thermal expansion. We assume that material is subject to two kinds of mechanical defor…
On unified theory for scalar conservation laws with fluxes and sources discontinuous with respect to the unknown
Miroslav Bulíček, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda
We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelt…
Regularity and Energy Conservation for the Compressible Euler Equations
Eduard Feireisl, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1
We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be c…