Journal of Mathematical Fluid Mechanics最新文献

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.

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.

The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting (m_e/m_irightarrow 0) and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.

In this paper, we show a mathematical justification of the data assimilation of nudging type in (L^p)-(L^q) maximal regularity settings. We prove that the approximate solution of the primitive equations constructed by the data assimilation converges to the true solution with exponential order in the Besov space (B^{2/q}_{q,p}(Omega )) for (1/p + 1/q le 1) on the periodic layer domain (Omega = mathbb {T}^2 times (-h, 0)).

In this paper, we study the wellposedness of the Cauchy problem for a non-conservative compressible two-fluid model with density-dependent viscosity coefficients vanishing at far field in three dimensions. The non-conservative pressure term (an implicit function) and the degenerate viscosity coefficients due to the vanishing of the volume fractions and the densities are the main issues. To overcome the difficulties, we construct iteration sequences in terms of the average densities and the velocities, and explore some new connections between the pressure term (including its gradients) and some other terms of the average densities. Those estimates are uniform for the positive lower bound of the average densities, and they are not trivial in particular when the adiabatic indexes are close to 1. Moreover, to get the strong convergence for the full sequences, one can not use the mean value theorem in the pressure term to get the desired estimates of the difference between the average densities due to the possible vanishing of the densities. Instead, we introduce some equations in terms of some new quantities associated with the volume fractions, the densities, and the average densities. Compared with the existing results on the same model, this work can be viewed as the first result on the wellposedness of regular solutions that allow the volume fraction and the density to vanish.

The aim of this paper is to design a feedback operator for stabilizing in infinite time horizon a system modeling the interactions between a viscous incompressible fluid and the deformation of a soap bubble. The latter is represented by an interface separating a bounded domain of (mathbb {R}^2) into two connected parts filled with viscous incompressible fluids. The interface is a smooth perturbation of the 1-sphere, and the surrounding fluids satisfy the incompressible Stokes equations in time-dependent domains. The mean curvature of the surface defines a surface tension force which induces a jump of the normal trace of the Cauchy stress tensor. The response of the fluids is a velocity trace on the interface, governing the time evolution of the latter, via the equality of velocities. The data are assumed to be sufficiently small, in particular the initial perturbation, that is the initial shape of the soap bubble is close enough to a circle. The control function is a surface tension type force on the interface. We design it as the sum of two feedback operators: one is explicit, the second one is finite-dimensional. They enable us to define a control operator that stabilizes locally the soap bubble to a circle with an arbitrary exponential decay rate, up to translations, and up to non-contact with the outer boundary.