We consider a multidimensional model for the dynamic combustion of compressible reacting fluids formulated by the Navier Stokes equations in Euler coordinates. For the chemical model we consider a one way irreversible chemical reaction governed by the Arrhenius kinetics. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is establish...

We study the compactness in Lloc of the semigroup (St)t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax [1]. Upper estimates for the Kolmogorov’s ε-entropy of the image through St of bounded sets C in L ∩ L∞ which is denoted by Hε(St(C) | L(R)) := log2 Nε(St(C)). where Nε(St(C)) is ...

We consider a kinetic BGK model relaxing to isentropic gas dynamics previously introduced by the authors, but with Dirichlet boundary condition on the incoming velocities. We pass to the limit as the relaxation parameter tends to zero by compensated compactness inside the domain, and obtain that the limit satisses entropy inequalities on the boundary involving weak traces of entropy uxes. Our m...

We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...

In this paper we characterize the boundedness, compactness, and weak compactness of integration operators $$\begin{aligned} T_g (f)(z)=\int _{0}^{z} f(w)g'(w)\ dw \end{aligned}$$ acting on average radial integrability spaces RM(p, q). For these purposes, develop different tools such as a description bidual 0) estimates norm using derivative functions, family results that call Littlewood–Paley t...

Compactness of the Neumann operator in the ∂̄-Neumann problem is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth domain is constructed for which condition (P) fails to hold, yet the Kohn Laplacian still has compact resolvent. The main result, in contrast, is that for smoothly bounded Hartogs domains, the well-known sufficient condition (P) is equivalent to ...

This paper investigates the existence of pure strategy, dominant strategy, and mixed strategy Nash equilibria in discontinuous and/or nonconvex games. We introduce a new notion of very weak continuity, called weak transfer quasi-continuity, which is weaker than the most known weak notions of continuity, including diagonal transfer continuity in Baye et al. [1993] and better-reply security in Re...

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In [1], an analogue of the Grothendieck compactness principle for the weak topology was used to characterize Banach spaces with the Schur property. Using a different analogue of the Grothendieck compactness principle for the weak topology...