Navier-Stokes Equations

By Tytti Saksa. Fundamentals of Ship Hydrodynamics, 2019

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Citations in the corpus

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows (2018, methodology): “Using the Aubin–Lions lemma [20], we derive that ui ! Ui strongly in L2(0, T ;H4 ) for any ✏ > 0.”
A Hybrid High-Order method for the incompressible Navier-Stokes equations based on Temam's device (2018, unknown): “Introduction In this work we propose a novel Hybrid High-Order (HHO) method for the incompressible Navier–Stokes equations based on a formulation of the convective term including Temam’s device for stability [1].”
Homogenization of the evolutionary Navier–Stokes system (2016, background): “1 Problem (1.1 - 1.4) is supplemented by the no-slip boundary conditions for the velocity u|∂Ωε = 0, (1.5) and the initial condition u(0, ·) = u0,ε. (1.6) As is well-known (see Leray [13], Hopf [11], Ladyzhenskaya [12], Temam [19], and many others), problem (1.1 - 1.6) possesses at least one weak so”
Convex integration and phenomenologies in turbulence (2019, background): “For an overview of the field we refer the reader to the classical texts [37, 191] and also to the books [56, 133, 22, 192, 79, 141, 126, 143, 127, 166, 193].”
Ergodic Theory of Infinite Dimensional Systems¶with Applications to Dissipative Parabolic PDEs (2002, background): “Most of the computations below are classically known (see for instance [2], [14]); we include them for completeness.”
On the uniqueness of weak solutions of the two-dimensional primitive equations (2003, result): “This result is in the same spirit as the result for the three dimensional Navier-Stokes equations, see [13], where a “weak/strong” uniqueness result is given, see also [14].”
Three dimensional system of globally modified Navier-Stokesequations with infinite delays (2010, background): “(5) We recall (see [21]) that there exists a constant C2 > 0 depending only on Ω such that |b(u, v, w)| ≤ C2‖u‖|Au|‖v‖|w|, (6) for all u ∈ D(A), v ∈ V,w ∈ H, and |b(u, v, w)| ≤ C2‖u‖‖v‖|w|‖w‖, (7) for all u, v, w ∈ V.”
On the regularity of a class of generalized quasi-geostrophic equations (2010, methodology): “ll satisfy the following energy inequality kθ(t)k2 L2(R2) +2ν Z t 0 kθ(τ)k2 H˙ β 2(R2) dτ≤ kθ0k2 L2(R2), t>0. (6.15) The proof follows from the standard process of establishing weak solutions (cf. [21, 17, 12]), and here we sketch it. Proof of Proposition 6.3. We consider the following approximat”
Stability results for 2D Navier–Stokes equations with unbounded delay (2018, background): “Owing to the fact that Navier-Stokes equations provide a suitable model to describe the motion of several important fluids, such as water, oil, air, etc, the long-time behavior of Navier-Stokes models (and its variants) has been regarded as an interesting and important problem in the theory of fluid”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “system does not admit a satisfactory solution theory up to now; beyond classical results on global weak solvability ([36], [53]), on local existence of smooth solutions ([15], [63]), and on absence of self-similar blow-up ([47]), the question of global solvability in classes of suitably regular func”
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement (2017, background): “24) Now since α > 34 , from a known embedding result ([15], [18]) we obtain that D(A ) →֒ L∞(Ω), so that invoking well-known smoothing properties of the analytic semigroup (e)t≥0 ([30], [13]) we infer from (10.”
On the energy equality for the 3D Navier–Stokes equations (2018, background): “The interest for very-weak solutions dates back to Foias [25], who proved their uniqueness under condition (1.3).”