Journal of Mathematical Fluid Mechanics最新文献

We study the symmetric stochastic p-Stokes system, (p in (1,infty )), in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost (-1/2) temporal derivatives on a Besov scale. Second, we verify that the velocity u of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient (V(mathbb {epsilon } u) = (kappa + left| mathbb {epsilon } uright| )^{(p-2)/2} mathbb {epsilon } u), (kappa ge 0), which measures the ellipticity of the p-Stokes system, has 1/2 temporal derivatives in a Nikolskii space.

Abstract

We propose a new concept of weak solutions to the multicomponent reactive flows driven by large boundary data. When the Gibbs’ equation incorporates the species mass fractions, we establish the global-in-time existence of weak solutions for any finite energy initial data. Moreover, if the classical solutions exist, the weak solutions coincide with them in the same time interval.

We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we adopt a monolithic approach to deduce (L^q)–(L^r) decay estimates of solutions to a non-autonomous linearized system. We then apply those estimates to the full nonlinear initial value problem to find temporal decay properties of the disturbance. Although the shape of the body is not allowed to be arbitrary, the present contribution is the first attempt at analysis of the large time behavior of solutions around nontrivial basic states, that can be time-dependent, for the fluid–structure interaction problem and provides us with a stability theorem which is indeed new even for steady motions under the self-propelling condition or with wake structure.

Motivated by Lu and Zhang (J Differ Equ 376:406–468, 2023), we prove the global existence of solutions to the three-dimensional isentropic compressible Navier–Stokes equations with smooth initial data slowly varying in two directions. In such a setting, the (L^2)-norms of the initial data are of order (O(varepsilon ^{-1})), which are large.

Abstract

In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of (L^2) -type.

We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and uniqueness of global smooth solutions and their convergence in the smooth regime to the Boussinesq solution when the regularizations are removed. We also consider a range of mixed (subcritical–supercritical) Voigt regularizations for which we prove the existence of global smooth solutions.

Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value/Cauchy problem of the one-dimensional pth power viscous reactive gas with positive constant viscosity, no result is available up to now for the corresponding problems with density-dependent viscosity. The main purpose of this paper is to study the global existence and asymptotic behavior of solutions to three types of initial-boundary value problems of 1d pth power viscous reactive gas with density-dependent viscosity and large initial data. The key ingredient in our analysis is to deduce the positive lower and upper bounds on both the specific volume and the absolute temperature.

Abstract

We consider the magnetohydrodynamics system with Hall effect accompanied with initial data in supercritical Sobolev space. Via an appropriate randomization of the supercritical initial data, both local and small data global well-posedness for the system are obtained almost surely in critical Sobolev space.

In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius.

A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier–Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, which triggers the migration of the endothelial cells and the blood vessel formation. The coupling of the equations is realized by the chemotaxis force in the momentum balance equation. The global existence of finite energy weak solutions is shown for adiabatic pressure coefficients (gamma >8/5). The solutions satisfy a relative energy inequality, which allows for the proof of the weak–strong uniqueness property.