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A rigorous justification of the Euler and Navier-Stokes equations with geometric effects
We derive the one-dimensional (1D) isentropic Euler and Navier--Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier--Stokes syst...
BA - Obecná matematika
- 2016 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system
for the isentropic Euler system. Under these circumstances the associated sequence of dissipative fluid governed by the Navier-Stokes system....
Pure mathematics
- 2021 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Contact discontinuities in multi-dimensional isentropic Euler equations
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 star...
Pure mathematics
- 2018 •
- Jimp
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
On uniqueness of dissipative solutions to the isentropic Euler system
The dissipative solutions can be seen as a convenient generalization of the concept of weak solution to the isentropic Euler system. They can be seen as expectations of the Young measures associated to a suitable measure-va...
Pure mathematics
- 2019 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Stability of the isentropic Riemann solutions of the full multidimensional Euler system
We consider the complete Euler system describing the time evolution of an invis- cid nonisothermal gas. We show that the rarefaction wave solutions of the one-dimensional (1-D) Riemann problem are stable, in particular unique, in th...
BA - Obecná matematika
- 2015 •
- Jx •
- Link
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Regularity and energy conservation for the compressible Euler equations
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 conserved. Our strategy relies on c...
Pure mathematics
- 2017 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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An overview of some recent results on the Euler system of isentropic gas dynamics
for the isentropic Euler system in two space dimensions have greater energy dissipation rate thanThis overview is concerned with the well-posedness problem for the isentropic compressible Euler equations ...
BA - Obecná matematika
- 2016 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
A note on the long-time behavior of dissipative solutions to the Euler system
We show that the Reynolds defect measure for a dissipative weak solution of the compressible Euler system vanishes for large time. This may be seen as a piece of evidence that the dissipative solutions are asymptotically close to we...
Pure mathematics
- 2021 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions
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 considered, namely to such a 2D Riemann problem for i...
Pure mathematics
- 2020 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Approximating viscosity solutions of the Euler system
Applying the concept of S-convergence, based on averaging in the spirit of Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler system are studied. We show how to efficiently compute a viscosity solution of th...
Pure mathematics
- 2022 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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