The Experts below are selected from a list of 5571 Experts worldwide ranked by ideXlab platform
Akitaka Matsumura - One of the best experts on this subject based on the ideXlab platform.
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asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes System
Archive for Rational Mechanics and Analysis, 2010Co-Authors: Feimin Huang, Jing Li, Akitaka MatsumuraAbstract:We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes System for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler System admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes System, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.
Jing Li - One of the best experts on this subject based on the ideXlab platform.
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asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes System
Archive for Rational Mechanics and Analysis, 2010Co-Authors: Feimin Huang, Jing Li, Akitaka MatsumuraAbstract:We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes System for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler System admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes System, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.
Feimin Huang - One of the best experts on this subject based on the ideXlab platform.
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stability of superposition of viscous contact wave and rarefaction waves for compressible navier stokes System
arXiv: Analysis of PDEs, 2015Co-Authors: Feimin Huang, Teng WangAbstract:This paper is concerned with the large-time behavior of solutions for the one-dimensional compressible Navier-Stokes System. We show that the combination of viscous contact wave with rarefaction waves for the non-isentropic polytropic gas is stable under \emph{large} initial perturbation without the condition that the adiabatic exponent $\gamma$ is close to 1, provided the strength of the combination waves is suitably small.
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asymptotic stability of combination of viscous contact wave with rarefaction waves for one dimensional compressible navier stokes System
Archive for Rational Mechanics and Analysis, 2010Co-Authors: Feimin Huang, Jing Li, Akitaka MatsumuraAbstract:We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes System for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler System admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes System, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.
Eduard Feireisl - One of the best experts on this subject based on the ideXlab platform.
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Homogenization of the evolutionary Navier-Stokes System
Manuscripta Mathematica, 2020Co-Authors: Eduard Feireisl, Yuliya Namlyeyeva, Šárka NečasováAbstract:We study the homogenization problem for the evolutionary Navier–Stokes System under the critical size of obstacles. Convergence towards the limit System of Brinkman’s type is shown under very mild assumptions concerning the shape of the obstacles and their mutual distance.
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Statistical Solutions to the Barotropic Navier–Stokes System
Journal of Statistical Physics, 2020Co-Authors: Francesco Fanelli, Eduard FeireislAbstract:We introduce a new concept of statistical solution in the framework of weak solutions to the barotropic Navier–Stokes System with inhomogeneous boundary conditions. Statistical solution is a family $$\{ M_t \}_{t \ge 0}$$ { M t } t ≥ 0 of Markov operators on the set of probability measures $$\mathfrak {P}[\mathcal {D}]$$ P [ D ] on the data space $$\mathcal {D}$$ D containing the initial data $$[\varrho _0, \mathbf{m}_0]$$ [ ϱ 0 , m 0 ] and the boundary data $$\mathbf{d}_B$$ d B . $$\{ M_t \}_{t \ge 0}$$ { M t } t ≥ 0 possesses a.a. semigroup property, $$\begin{aligned} M_{t + s}(\nu ) = M_t \circ M_s(\nu ) \ \text{ for } \text{ any }\ t \ge 0, \ \text{ a.a. }\ s \ge 0, \ \text{ and } \text{ any }\ \nu \in \mathfrak {P}[\mathcal {D}]. \end{aligned}$$ M t + s ( ν ) = M t ∘ M s ( ν ) for any t ≥ 0 , a.a. s ≥ 0 , and any ν ∈ P [ D ] . $$\{ M_t \}_{t \ge 0}$$ { M t } t ≥ 0 is deterministic when restricted to deterministic data, specifically $$\begin{aligned} M_t( \delta _{[\varrho _0, \mathbf{m}_0, \mathbf{d}_B]}) = \delta _{[\varrho (t, \cdot ), \mathbf{m}(t, \cdot ), \mathbf{d}_B]},\ t \ge 0, \end{aligned}$$ M t ( δ [ ϱ 0 , m 0 , d B ] ) = δ [ ϱ ( t , · ) , m ( t , · ) , d B ] , t ≥ 0 , where $$[\varrho , \mathbf{m}]$$ [ ϱ , m ] is a finite energy weak solution of the Navier–Stokes System corresponding to the data $$[\varrho _0, \mathbf{m}_0, \mathbf{d}_B] \in \mathcal {D}$$ [ ϱ 0 , m 0 , d B ] ∈ D . $$M_t: \mathfrak {P}[\mathcal {D}] \rightarrow \mathfrak {P}[\mathcal {D}]$$ M t : P [ D ] → P [ D ] is continuous in a suitable Bregman–Wasserstein metric at measures supported by the data giving rise to regular solutions.
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Statistical solutions to the barotropic Navier-Stokes System
arXiv: Analysis of PDEs, 2020Co-Authors: Francesco Fanelli, Eduard FeireislAbstract:We introduce a new concept of statistical solution in the framework of weak solutions to the barotropic Navier--Stokes System with inhomogeneous boundary conditions. Statistical solution is a family $\{ M_t \}_{t \geq 0}$ of Markov operators on the set of probability measures $\mathfrak{P}[\mathcal{D}]$ on the data space $\mathcal{D}$ containing the initial data $[\varrho_0, \mathbf{m}_0]$ and the boundary data $\mathbf{d}_B$. (1) $\{ M_t \}_{t \geq 0}$ possesses a.a. semigroup property, $ M_{t + s}(\nu) = M_t \circ M_s(\nu)$ for any $t \geq 0$, a.a. $s \geq 0$, and any $\nu \in \mathfrak{P}[\mathcal{D}]$. (2) $\{ M_t \}_{t \geq 0}$ is deterministic when restricted to deterministic data, specifically $ M_t(\delta_{[\varrho_0, \mathbf{m}_0, \mathbf{d}_B]}) = \delta_{[\varrho(t, \cdot), \mathbf{m}(t, \cdot), \mathbf{d}_B]}, $ where $[\varrho, \mathbf{m}]$ is a finite energy weak solution of the Navier--Stokes System corresponding to the data $[\varrho_0, \mathbf{m}_0, \mathbf{d}_B] \in \mathcal{D}$. (3) $M_t: \mathfrak{P}[\mathcal{D}] \to \mathfrak{P}[\mathcal{D}]$ is continuous in a suitable Bregman--Wasserstein metric at measures supported by the data giving rise to regular solutions.
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Markov selection for the stochastic compressible Navier--Stokes System
arXiv: Probability, 2018Co-Authors: Dominic Breit, Eduard Feireisl, Martina HofmanováAbstract:We analyze the Markov property of solutions to the compressible Navier--Stokes System perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in [F. Flandoli, M. Romito: Markov selections for the 3D stochastic Navier--Stokes equations. Probab. Theory Relat. Fields 140, 407--458. (2008)]. A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time. In addition, it cannot be recovered from the variables whose time evolution is described by the Navier--Stokes System, namely, the density and the momentum. We overcome this issue by introducing an auxiliary variable into the Markov selection procedure.
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Stationary solutions to the compressible Navier–Stokes System with general boundary conditions
Annales de l'Institut Henri Poincaré C Analyse non linéaire, 2018Co-Authors: Eduard Feireisl, Antonín NovotnýAbstract:Abstract We consider the stationary compressible Navier–Stokes System supplemented with general inhomogeneous boundary conditions. Assuming the pressure to be given by the standard hard sphere EOS we show existence of weak solutions for arbitrarily large boundary data.
Antonín Novotný - One of the best experts on this subject based on the ideXlab platform.
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compressible navier stokes System with hard sphere pressure law and general inflow outflow boundary conditions
Journal of Differential Equations, 2019Co-Authors: Hi Jun Choe, Antonín Novotný, Minsuk YangAbstract:Abstract We prove the existence of a weak solution to the compressible Navier–Stokes System with hard sphere possibly non-monotone pressure law involving, in particular, the Carnahan–Starling model [2] largely employed in various physical and industrial applications. We take into account large velocities prescribed at the boundary of a bounded piecewise C 2 domain and large densities prescribed at the inflow boundary without any restriction neither on the shape of the inflow/outflow boundaries nor on the shape of the domain.
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Stationary solutions to the compressible Navier–Stokes System with general boundary conditions
Annales de l'Institut Henri Poincaré C Analyse non linéaire, 2018Co-Authors: Eduard Feireisl, Antonín NovotnýAbstract:Abstract We consider the stationary compressible Navier–Stokes System supplemented with general inhomogeneous boundary conditions. Assuming the pressure to be given by the standard hard sphere EOS we show existence of weak solutions for arbitrarily large boundary data.
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Robustness of strong solutions to the compressible Navier-Stokes System
Mathematische Annalen, 2015Co-Authors: Peter Bella, Eduard Feireisl, Antonín NovotnýAbstract:We consider the Navier-Stokes System describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier’s slip boundary conditions. It is shown that the class of global in time strong solutions is robust with respect to small perturbations of the initial data. Explicit qualitative estimates are given also in terms of the shape of the underlying physical domain, with applications to problems posed on thin cylinders.
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On incompressible limits for the Navier-Stokes System on unbounded domains under slip boundary conditions
Discrete and Continuous Dynamical Systems-series B, 2010Co-Authors: Donatella Donatelli, Eduard Feireisl, Antonín NovotnýAbstract:We study the low Mach number limit for the compressible Navier-Stokes System supplemented with Navier's boundary condition on an unbounded domain with compact boundary. Our main result asserts that the velocities converge pointwise to a solenoidal vector field - a weak solution of the incompressible Navier-Stokes System - while the fluid density becomes constant. The proof is based on a variant of local energy decay property for the underlying acoustic equation established by Kato.
