Euler system
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Global III-posedness of the isentropic system of gas dynamics Open
We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p ($\rho$) = $\rho$$^2$ and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are inf…
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Anomalous dissipation for 1/5-Hölder Euler flows Open
Recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in Hölder spaces. The motivation comes from Onsager’s conjecture. The construction involves a super…
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Study of a New Asymptotic Preserving Scheme for the Euler System in the Low Mach Number Limit Open
This paper deals with the discretization of the compressible Euler system for all Mach number regimes. For highly subsonic flows, since acoustic waves are very fast compared to the velocity of the fluid, the gas can be considered as incomp…
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An energy-consistent depth-averaged Euler system: Derivation and properties Open
In this paper, we present an original derivation process of a non-hydrostatic\nshallow water-type model which aims at approximating the incompressible Euler\nand Navier-Stokes systems with free surface. The closure relations are obtained\n…
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From gas dynamics with large friction to gradient flows describing diffusion theories Open
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flo…
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Measure-valued solutions to the complete Euler system Open
We introduce the concept of dissipative measure-valued solution to the complete Euler system describing the motion of an inviscid compressible fluid. These solutions are characterized by a parameterized (Young) measure and a dissipation de…
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Asymptotic Behavior of Solutions to Euler Equations with Time-Dependent Damping in Critical Case Open
In this paper, we are concerned with the system of Euler equations with time-dependent damping like $-\frac{\mu}{(1+t)^\lambda}u$ for physical parameters $\lambda\ge 0$ and $\mu>0$. It is well known that, when $0\le \lambda<1$, the time-as…
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Mapped Tent Pitching Schemes for Hyperbolic Systems Open
Diese Arbeit behandelt eine Lösungsmethode für zeitabhängige hyperbolische Probleme, wie zum Beispiel die Maxwell- oder Eulergleichungen. Hyperbolische Probleme haben eine wohldefinierte Ausbreitungsgeschwindigkeit, welche im Weiteren dazu…
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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…
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Partially dissipative one-dimensional hyperbolic systems in the critical regularity setting, and applications Open
Here we develop a method for investigating global strong solutions of partially dissipative hyperbolic systems in the critical regularity setting. Compared to the recent works by Kawashima and Xu, we use hybrid Besov spaces with different …
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On the Low Mach Number Limit for the Compressible Euler System Open
In this paper, we propose a new approach to singular limits of inviscid fluid\nflows based on the concept of dissipative measure-valued solutions. We show\nthat dissipative measure-valued solutions of the compressible Euler equations\nconv…
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Three-Dimensional Full Euler Flows with Nontrivial Swirl in Axisymmetric Nozzles Open
We are concerned with the unique existence of three-dimensional steady compressible full Euler flows through arbitrary infinitely long axisymmetric and piecewise smooth nozzles with nontrivial swirl. We develop a new approach to prove the …
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EULER SYSTEMS FOR HILBERT MODULAR SURFACES Open
We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conjecture of Bloch and Kato on injectivity of regulator maps holds, t…
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Expansion of a compressible gas in vacuum Open
Tai-Ping Liu \cite{Liu\_JJ} introduced the notion of "physical solution' of the isentropic Euler system when the gas is surrounded by vacuum. This notion can be interpreted by saying that the front is driven by a force resulting from a Höl…
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On the initial boundary value problem of a Navier-Stokes/$Q$-tensor model for liquid crystals Open
This work is concerned with the solvability of a Navier-Stokes/Q-tensor coupled system modeling the nematic liquid crystal flow on a bounded domain in three dimensional Euclidian space with strong anchoring boundary condition for the order…
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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…
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Asymptotic Stability of Rarefaction Wave for the Inflow Problem Governed by the One-Dimensional Radiative Euler Equations Open
This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic…
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Iwasawa theory for the symmetric square of a modular form Open
We construct a compatible family of global cohomology classes (an Euler system) for the symmetric square of a modular form, and apply this to bounding Selmer groups of the symmetric square Galois representation and its twists.
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Iwasawa theory for Rankin-Selberg products ofp-nonordinary eigenforms Open
Let f and g be two modular forms which are non-ordinary at p. The theory of Beilinson-Flach elements gives rise to four rank-one non-integral Euler systems for the Rankin-Selberg convolution f⊗g, one for each choice of p-stabilisations of …
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Periods in the Use of Euler-Type Diagrams Open
Logicians commonly speak in a relatively undifferentiated way about pre-Euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which Euler-type diagrams (line diagrams as well as circ…
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Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations Open
We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that ther…
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Large-time behavior of solutions to Cauchy problem for bipolar Euler–Poisson system with time-dependent damping in critical case Open
This paper is concerned with the Cauchy problem of a bipolar hydrodynamic model for semiconductor device, a system of one dimensional Euler-Poisson equations with time-dependent damping effect in the critical case.The global existence and …
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Sonic-supersonic solutions for the two-dimensional pseudo-steady full Euler equations Open
This paper is focused on the existence of classical sonic-supersonic solutions near sonic curves for the two-dimensional pseudo-steady full Euler equations in gas dynamics. By introducing a novel set of change variables and using the idea …
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The compressible Euler equations in a physical vacuum: A comprehensive Eulerian approach Open
This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical …
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On similarity flows for the compressible Euler system Open
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows, t…
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Anticyclotomic Iwasawa theory of elliptic modular forms at non-ordinary primes Open
This article is a continuation of our previous work on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formula…
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Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and various applications Open
\nThis paper provides the full proof of the results announced by the authors in [C. R. Acad. Sciences (2016)]. We introduce an original relative entropy for compressible Navier-Stokes equations with density dependent viscosities and discus…
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Exact solution and the multidimensional Godunov scheme for the acoustic equations Open
The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming a…
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A proof of Perrin-Riou’s Heegner point mainconjecture Open
Let $E/\mathbf{Q}$ be an elliptic curve of conductor $N$, let $p>3$ be a prime where $E$ has good ordinary reduction, and let $K$ be an imaginary quadratic field satisfying the Heegner hypothesis. In 1987, Perrin-Riou formulated an Iwasawa…
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Blow-up for compressible Euler system with space-dependent damping in 1-D Open
This article considers the Cauchy problem for compressible Euler system in R {\bf{R}} with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and…