Ondřej Kreml
YOU?
Author Swipe
View article: Interpreting convex integration results in hydrodynamics
Interpreting convex integration results in hydrodynamics Open
The aim of this article is to encourage debate of issues of the applications of modern methods of mathematical analysis in fluid dynamics. A recent surprising result derived by convex integration techniques shows non-uniqueness of weak sol…
View article: Steady compressible Navier-Stokes-Fourier system with general temperature dependent viscosities I: density estimates based on Bogovskii operator
Steady compressible Navier-Stokes-Fourier system with general temperature dependent viscosities I: density estimates based on Bogovskii operator Open
The aim of this paper is to reconsider the existence theory for steady compressible Navier--Stokes--Fourier system assuming more general condition of the dependence of the viscosities on the temperature in the form $μ(\vartheta)$, $ξ(\vart…
View article: On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams
On time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams Open
In this paper, we study a nonlinear fluid-structure interaction problem between a viscoelastic beam and a compressible viscous fluid. The beam is immersed in the fluid which fills a two-dimensional rectangular domain with periodic boundary…
View article: Measure-valued solutions and weak-strong uniqueness for the\n incompressible inviscid fluid-rigid body interaction
Measure-valued solutions and weak-strong uniqueness for the\n incompressible inviscid fluid-rigid body interaction Open
We consider a coupled system of partial and ordinary differential equations\ndescribing the interaction between an isentropic inviscid fluid and a rigid\nbody moving freely inside the fluid. We prove the existence of measure-valued\nsoluti…
View article: Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data
Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data Open
We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the …
View article: Nonuniqueness of Admissible Weak Solution to the Riemann Problem for the Full Euler System in Two Dimensions
Nonuniqueness of Admissible Weak Solution to the Riemann Problem for the Full Euler System in Two Dimensions Open
The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were co…
View article: Dissipative measure-valued solutions for general conservation laws
Dissipative measure-valued solutions for general conservation laws Open
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. This means that they coincide with a strong solution emanatin…
View article: Compressible Navier-Stokes system on a moving domain in the $L_p-L_q$ framework
Compressible Navier-Stokes system on a moving domain in the $L_p-L_q$ framework Open
We prove the local well-posedness for the barotropic compressible Navier-Stokes system on a moving domain, a motion of which is determined by a given vector field ${\bf V}$, in a maximal $L_p-L_q$ regularity framework. Under additional sma…
View article: Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains
Local existence of strong solutions and weak–strong uniqueness for the compressible Navier–Stokes system on moving domains Open
We consider the compressible Navier–Stokes system on time-dependent domains with prescribed motion of the boundary. For both the no-slip boundary conditions as well as slip boundary conditions we prove local-in-time existence of strong sol…
View article: Non-uniqueness of admissible weak solutions to the compressible Euler\n equations with smooth initial data
Non-uniqueness of admissible weak solutions to the compressible Euler\n equations with smooth initial data Open
We consider the isentropic Euler equations of gas dynamics in the whole\ntwo-dimensional space and we prove the existence of a $C^\\infty$ initial datum\nwhich admits infinitely many bounded admissible weak solutions. Taking\nadvantage of …
View article: Contact discontinuities in multi-dimensional isentropic euler equations
Contact discontinuities in multi-dimensional isentropic euler equations Open
In this note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove non-uniqueness of admissible weak solutions that start from …
View article: Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations
Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations Open
We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhi…
View article: Local existence of strong solutions and weak-strong uniqueness for the\n compressible Navier-Stokes system on moving domains
Local existence of strong solutions and weak-strong uniqueness for the\n compressible Navier-Stokes system on moving domains Open
We consider the compressible Navier-Stokes system on time-dependent domains\nwith prescribed motion of the boundary. For both the no-slip boundary\nconditions as well as slip boundary conditions we prove local-in-time existence\nof strong …
View article: Flow of heat conducting fluid in a time dependent domain
Flow of heat conducting fluid in a time dependent domain Open
We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier-Stokes-Fourier system consisting of equation of continuity, momentum balance, entropy bal…
View article: On contact discontinuities in multi-dimensional isentropic Euler equations
On contact discontinuities in multi-dimensional isentropic Euler equations Open
In this short note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove nonuniqueness of admissible weak solutions that start …
View article: Weak-strong uniqueness for compressible Navier-Stokes system with slip boundary conditions on time dependent domains
Weak-strong uniqueness for compressible Navier-Stokes system with slip boundary conditions on time dependent domains Open
We consider the compressible Navier-Stokes system on time-dependent domains with prescribed motion of the boundary, supplemented with slip boundary conditions for the velocity. We derive the relative entropy inequality in the spirit of Fei…
View article: Weak-strong uniqueness for compressible Navier-Stokes system with slip\n boundary conditions on time dependent domains
Weak-strong uniqueness for compressible Navier-Stokes system with slip\n boundary conditions on time dependent domains Open
We consider the compressible Navier-Stokes system on time-dependent domains\nwith prescribed motion of the boundary, supplemented with slip boundary\nconditions for the velocity. We derive the relative entropy inequality in the\nspirit of …