A Data Assimilation Algorithm for the Subcritical Surface Quasi-Geostrophic Equation
Advanced Nonlinear Studies, 2017 In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary.
Jolly Michael S. +2 more
doaj +1 more source
Optimality of Serrin type extension criteria to the Navier-Stokes equations
Advances in Nonlinear Analysis, 2021 We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
doaj +1 more source
Short-time existence of a quasi-stationary fluid–structure interaction problem for plaque growth
Advances in Nonlinear Analysis, 2023 We address a quasi-stationary fluid–structure interaction problem coupled with cell reactions and growth, which comes from the plaque formation during the stage of the atherosclerotic lesion in human arteries.
Abels Helmut, Liu Yadong
doaj +1 more source
An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations
, 2009 We prove existence of weak martingale solutions satisfying an almost sure version of the energy inequality and which constitute a (almost sure) Markov process.Comment: Submitted for the proceedings of the conference "Stochastic partial differential ...
Romito, Marco
core +1 more source
A Liouville theorem for the Degasperis-Procesi equation [PDF]
, 2015 We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point (t0, x0), is the identically zero solution.
Brandolese, Lorenzo
core
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
, 2018 The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization.
AJ Chorin +37 more
core +1 more source
Asymptotic analysis of Leray solution for the incompressible NSE with damping
Demonstratio MathematicaIn 2008, Cai and Jiu showed that the Cauchy problem of the Navier-Stokes equations, with damping α∣u∣β−1u\alpha {| u| }^{\beta -1}u for α>0\alpha \gt 0 and β≥1\beta \ge 1 has global weak solutions in L2(R3){L}^{2}\left({{\mathbb{R}}}^{3}).
Blel Mongi, Benameur Jamel
doaj +1 more source
Local stability of energy estimates for the Navier--Stokes equations
, 2017 We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the ...
Chamorro, Diego +2 more
core +1 more source
Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions
, 2011 The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain.
Bresch D +10 more
core +1 more source
Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Advanced Nonlinear Studies, 2018 This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
doaj +1 more source