In this paper we consider the regularity problem of Navier–Stokes equations in $$ {\mathbb {R}}^{3} . We show that Serrin-type condition imposed on one component velocity u_3\in L^p(0,T; L^q({\mathbb ))$$ with \frac{2}{p}+ \frac{3}{q} <1$$ , 3<q \le +\infty implies weak Leray solution u: \times (0,T) \rightarrow initial data belonging to L^2({\mathbb {R}}^3) \cap L^3({\mathbb {R}}^{3})$$ The re...

In this paper a computational method is presented for predicting the unsteady hydrodynamic forces acting on partial immersed propeller (SPP). In order to simulate the unsteady viscous flow around a SPP, a Reynolds-Averaged Navier&ndash;Stokes (RANS) solver is used. The time-accurate calculations are made by applying the sliding mesh method. Structured and unstructured mesh techniques are used. ...

We present a loosely coupled, partitioned scheme for solving fluid–structure interaction (FSI) problems with the Navier slip boundary condition. The fluid flow is modeled by Navier–Stokes equations an incompressible, viscous fluid, interacting thin elastic structure membrane or Koiter shell type equations. and are coupled via two sets of coupling conditions: dynamic condition describing balance...

For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flowfield and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equatio...

In this paper, we consider the conditional regularity of weak solution to 3D Navier–Stokes equations. More precisely, prove that if one directional derivative velocity, say ?3u, satisfies ?3u?Lp0,1(0,T;Lq0(R3)) with 2p0+3q0=2 and 32<q0<+?, then is regular on (0,T]. The proof based new local energy estimates introduced by Chae-Wolf (2019) [4] Wang-Wu-Zhang (2020) [21].

In this work, rising of a single bubble in a quiescent liquid under microgravity condition was simulated. The related unsteady incompressible full Navier-Stokes equations were solved using a conventional finite difference method with a structured staggered grid. The interface was tracked explicitly by connected marker points via hybrid front capturing and tracking method. One field approximatio...

Optimal control and optimal shape design problems for the Navier-Stokes equations arise in many important practical applications, such as design of optimal profiles [7], drag minimization [9], [11], and heating and cooling [12], among others. Typically, optimal control problems for the NavierStokes equations combine Lagrange multiplier techniques to enforce the constraints and to derive an opti...

We develop a general method that allows to show the existence of spectral gaps for Markov semigroups on Banach spaces. Unlike most previous work, the type of norm we consider for this analysis is neither a weighted supremum norm nor an L-type norm, but involves the derivative of the observable as well and hence can be seen as a type of 1–Wasserstein distance. This turns out to be a suitable app...

The aerodynamics of hovering flight in a hawkmoth (Manduca sexta) are examined using a computational modelling approach which combines a low-fidelity bladeelement model with a high-fidelity Navier–Stokes-based flow solver. The focus of the study is on understanding the optimality of the hawkmoth-inpired wingstrokes with respect to lift generation and power consumption. The approach employs a ti...