On compactness of solutions to the compressible isentropic Navier-Stokes equations when the density is not square integrable Abstract. We show compactness of bounded sets of weak solutions to the isentropic compressible Navier-Stokes equations in three space dimensions under the hypothesis that the adiabatic constant γ > 3/2.

In this paper, the theory of Oθ-convergence and weak Oθ-convergence of nets is introduced in L-spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi’s O-convergence. It can be used to characterize preclosed sets, preopen sets, θ-closed sets, θ-open sets, almost F -compactness and almost S-compactness.

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in L∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The L∞ uniform estimate and H−1 compactness are ...

Recently, Girardi gave a characterization of relative strong L 1 R-compactness in terms of relative weak L 1 R-compactness and the Bocce criterion 18]. Here this result is generalized and extended by presenting a less stringent oscillation restriction condition (ORC) which enforces the transcendence of weak into an appropiately reformulated form of strong convergence in L 1 E , for E a separabl...

Abstract We prove a correspondence between $\kappa$ -small fibrations in simplicial presheaf categories equipped with the injective or projective model structure (and left Bousfield localizations thereof) and relatively -compact maps their underlying quasi-categories for suitably large regular cardinals . thus obtain transition result weakly universal small (type-theoretic) Dugger–Rezk-style st...

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the n-dimensional(n ≥ 2) Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy H−1 loc (Ω) compactness conditions. As illustration, we show the existence...