1,721,060 research outputs found
A Limiting Viscosity Approach for the Riemann Problem in Isentropic Gas Dynamics
No full textSlemrod, Marshall; Tzavaras, Athanasios E.. (1989). A Limiting Viscosity Approach for the Riemann Problem in Isentropic Gas Dynamics. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/5077
From gas dynamics with large friction to gradient flows describing diffusion theories
No full textWe 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 flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.AET was supported by funding from King Abdullah University of Science and
Technology (KAUST)
Two-dimensional transport equation with Hamiltonian vector fields
Full text linkWe illustrate the main steps in the proof of a sharp result of well-posedness for the two-dimensional transport equation whose vector field is bounded, autonomous, divergence free and satisfies the so-called "weak Sard property".
We also remark on the fact that the weak Sard property we identify is indeed equivalent to well-posedness
ABSENCE OF ANOMALOUS DISSIPATION FOR WEAK SOLUTIONS OF THE MAXWELL–STEFAN SYSTEM
No full textIn this paper we give a short and self-contained proof of the fact that weak solutions to the Maxwell-Stefan system automatically satisfy an entropy equality, establishing the absence of anomalous dissipation
Modellierung und Analysis von Multikomponentensystemen für Gasmischungen
Full text linkThe aim of this thesis is to understand and analyze diffussive and thermal effects in multicomponent systems for gas mixtures through the perspective of partial differential equations. Starting from Class–II models of thermodynamics,diffusion equations are derived formally by a Chapman–Enskog expansion and the expansion is justified as a relaxation limit by means of the relative entropy method.Das Ziel dieser Arbeit ist das Verständnis und die Analyse von diffusiven und thermischen Effekten in Mehrkomponentensystemen für Gasgemische aus der Perspektive partieller Differentialgleichungen. Ausgehend von Klasse-II-Modellen der Thermodynamik,werden Diffusionsgleichungen formal durch eine Chapman-Enskog-Erweiterung abgeleitet und die Expansion wird als Relaxationsgrenze mit Hilfe der Methode der relativen Entropie Methode begründet
Alignment via Friction for Nonisothermal Multicomponent Fluid Systems
No full textThe derivation of an approximate Class–I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class–II model is justified, by validating the Chapman–Enskog expansion performed from the Class–II model towards the Class–I model. The analysis proceeds by comparing two thermomechanical theories via relative entropy.Research partially supported by King Abdullah University of Science and Technology (KAUST) baseline funds. The first author acknowledges partial support from the Austrian Science Fund (FWF), grants P33010 and F65. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, ERC Advanced Grant no. 101018153
Stability properties of the Euler-Korteweg system with nonmonotone pressures
No full textWe establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.JG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’
Oscillations in compressible Navier–Stokes and homogenization in phase transition problems
No full textIn the first part of this paper we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier–Stokes system with non-monotone pressure. This part complements [A. E. Tzavaras, Sustained oscillations in hyperbolic-parabolic systems, Arch. Ration. Mech. Anal. 248 (2024) 51] where such examples are extensively studied. The second part deals with the problem of homogenization for one-dimensional models describing phase transitions for viscoelastic materials. Ideas from the kinetic formulation of conservation laws are employed to derive effective equations that describe the propagation of oscillations
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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