1,721,106 research outputs found
Existence and stability of strong solutions to the Abels–Garcke–Grün model in three dimensions
Full text linkThis work is devoted to the analysis of the strong solutions to the Abels–Garcke–Grün (AGG) model in three dimensions. First, we prove the existence of local-in-time strong solutions originating from an initial datum (u_0, φ_0) ∊ H^1_α × H^2(Ω) such that μ_0 ∈ H^1(Ω) and ∣φ_0∣ ≤ 1. For the subclass of initial data that are strictly separated from the pure phases, the corresponding strong solutions are locally unique. Finally, we show a stability estimate between the solutions to the AGG model and the model H. These results extend the analysis achieved by the author in 2021 from two-dimensional bounded domains to three-dimensional ones
Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities
Full text linkWe study the Abels–Garcke–Grün (AGG) model for a mixture of two viscous incompressible fluids with different densities. The AGG model consists of a Navier–Stokes–Cahn–Hilliard system characterized by a (non-constant) concentration-dependent density and an additional flux term due to interface diffusion. In this paper we address the well-posedness problem in the two-dimensional case. We first prove the existence of local strong solutions in general bounded domains. In the space periodic setting we show that the strong solutions exist globally in time. In both cases we prove the uniqueness and the continuous dependence on the initial data of the strong solutions. Lastly, we show a stability result for the strong solutions to the AGG model and the model H in terms of the density values
ATTRACTORS FOR THE NAVIER-STOKES-CAHN-HILLIARD SYSTEM
No full textWe investigate the longtime behavior of the solutions to the Navier-Stokes-Cahn-Hilliard system (also known as Model H) with singular (e.g. Flory-Huggins) potential and non-constant viscosity. We prove that the initial and boundary value problem generates a strongly continuous semigroup on a suitable phase-space. Next, we establish the existence of the global attractor and of exponential attractors, and their regularity properties
Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations
No full textWe analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with the observed, spatially coarse data. This synchronization holds even though it is not known whether the reference solution, with initial data in L-2, is unique; any particular reference solution is determined by the observed, coarse data. The efficacy of the algorithm in both 2D and 3D is demonstrated by numerical computations. (C) 2022 The Author(s). Published by Elsevier Ltd
Correction to: Pediatric elbow arthroscopy: clinical outcomes and complications after long-term follow-up (Journal of Orthopaedics and Traumatology, (2021), 22, 1, (55), 10.1186/s10195-021-00619-2)
No full textFollowing publication of the original article [1], the authors identified an error in the author names. The given name and family name were erroneously transposed. The incorrect author names: Micheloni Gian Mario, Tarallo Luigi, Negri Alberto, Giorgini Andrea, Merolla Giovanni and Porcellini Giuseppe. The correct author names: Gian Mario Micheloni, Luigi Tarallo, Alberto Negri, Andrea Giorgini, Giovanni Merolla, Giuseppe Porcellini. The author group has been updated above and the original article [1] has been corrected
The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures
No full textWe study the well-posedness for the mildly compressible Navier- Stokes-Cahn-Hilliard system with non-constant viscosity and Landau potential in two and three dimensional domains
THE SEPARATION PROPERTY FOR 2D CAHN-HILLIARD EQUATIONS: LOCAL, NONLOCAL AND FRACTIONAL ENERGY CASES
No full textWe study the separation property for Cahn-Hilliard type equations with constant mobility and (physically relevant) singular potentials in two dimensions. That is, any solution with initial finite energy stays uniformly away from the pure phases +/- 1 from a certain time on. Beyond its physical interest, this property plays a crucial role to achieve high order Sobolev and analytic regularity of the solutions and to analyze their longtime behavior. In the local case, we streamline known arguments by exploiting the Sobolev inequality to obtain direct entropy estimates. In the nonlocal case, we provide a new proof based on De Giorgi estimates rather than the Alikakos-Moser type argument. Finally, in the spectral-fractional case, we prove nonlinear estimates and the separation property for any fractional index s is an element of (0,1) filling the gap between first-order (local) and zero-order (nonlocal) energy cases. In all of the aforementioned cases, our new proofs neither make use of the Trudinger-Moser inequality nor of any assumptions involving the third derivative of the entropy, as in the previous contributions. In particular, they apply for a more general class of singular potentials than the Flory-Huggins (Boltzmann-Gibbs) logarithmic density. Besides, the new methods present a series of technical advantages, which can be useful to the analysis of important physical systems that couple Cahn-Hilliard equations with other equations (e.g., reaction-diffusion equations and/or Navier-Stokes type systems) as well as their stochastic counterparts
Erythrocyte redox state in uremic anemia: effects of hemodialysis and relevance of glutathione metabolism.
No full textVolar PEEK plate for distal radial fracture: analysis of plate ruptures in a group of 120 patients
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