Journal of Mathematical Fluid Mechanics最新文献

In this note, we show two results in the setting of Galdi-Silvestre strong solutions for the rigid body-viscous fluid interaction. The former, under an additional integrability assumption on the gradient of the initial datum, proves that the time derivative of the solution belongs to (L^2(0,T;L^2(Omega ))). The latter, thanks to a further assumption only on one solution, proves that the uniqueness holds in the quoted setting. However, our extra assumption for the uniqueness is certainly verified under the integrability assumption on the gradient of the initial datum. Hence, the set of solutions enjoying the uniqueness is not empty.

In this article, we investigate the nonlinear stability of the Couette flow under the Boussinesq equations with only vertical dissipation in ({mathbb {T}}times {mathbb {R}}). Inspired by the work of Wei and Zhang [Tunis. J. Math. 5(3):573-592 (2023)] and taking into account perturbations with different sizes, we can address the influence of buoyancy term within the coupled system. We obtain a stability result under the initial perturbations condition: (Vert omega ^{(0)}Vert _{H^b}+nu ^{-1/2}Vert theta ^{(0)}Vert _{H^b}+nu ^{-1/6}Vert partial _xtheta ^{(0)}Vert _{H^b}lesssim nu ^{1/3}), where (bge 2).

In this paper, we control the growth of the support of particular solutions to the Euler two-dimensional equations, whose vorticity is concentrated near special vortex crystals. These vortex crystals belong to the classical family of regular polygons with a central vortex, where we choose a particular intensity for the central vortex to have strong stability properties. A special case is the regular pentagon with no central vortex which also satisfies the stability properties required for the long-time confinement to work.

We prove that there exists a weak solution of the Stokes system with a non-zero external force and no-slip boundary conditions in a half-space of dimension three or higher such that its normal derivatives are unbounded near the boundary. A localized, divergence-free singular force causes, via a non-local effect, singular behavior of normal derivatives of the solution near the boundary, although this boundary is away from the support of the external force. The constructed solution is a weak solution with finite global energy, and it (can be compared to the one in Seregin and S̆verák (Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 385 (2010), Kraevye Zadachi Matematicheskoĭ Fiziki i Smezhnye Voprosy Teorii Funktsiĭ. 41, 200–205, 236; J. Math. Sci. 178, no. 3, 353–356 (2011)), which is a form of shear flow with only locally finite energy. A similar construction is performed) for the Navier-Stokes equations as well.

Starting from the governing equations for geophysical flows, by means of a thin-shell approximation and a tangent plane approximation, we derive the equations describing, at leading order, the nonlinear ice-drift flow for regions centered around the North Pole. An exact solution is derived in the material/Lagrangian formalism, describing a superposition of oscillations, a mean Ekman flow, and a geostrophic current.

In this paper, we study the global existence for a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the critical cell density satisfies (P'(bar{rho })=frac{amu }{b}bar{rho }), we establish the global existence for small perturbations and derive the optimal convergent rates for all-order derivatives of the solution.

Under the shallow-water regime and without assuming wave amplitude smallness, we apply the variational approach in the Lagrangian formalism to derive the geophysical Green-Naghdi system. In contrast to the prior derivation in (Fan et al., J. Nonlinear Sci., 32(21), 30 (2022)) that imposed a columnar-flow Ansatz, our method adopts the irrotational-flow assumption (which Fan et al., J. Nonlinear Sci., 32(21), 30 (2022) does not), thereby generating the depth-independent horizontal velocity at leading order.

We are concerned with the global existence and vanishing dispersion limit of strong/classical solutions to the Cauchy problem of the one-dimensional isentropic compressible quantum Navier-Stokes equations, which consists of the compressible Navier-Stokes equations with a linearly density-dependent viscosity and a nonlinear third-order differential operator known as the quantum Bohm potential. The pressure (p(rho )=rho ^gamma ) is considered with (gamma ge 1) being a constant. We focus on the case when the Planck constant (varepsilon ) and the viscosity constant (nu ) are not equal. Under some suitable assumptions on (varepsilon , nu , gamma ), and the initial data, we proved the global existence and large-time behavior of strong and classical solutions away from vacuum to the compressible quantum Navier-Stokes equations with arbitrarily large initial data. This result extends the previous ones on the construction of global strong large-amplitude solutions of the compressible quantum Navier-Stokes equations to the case (varepsilon ne nu ). Moreover, the vanishing dispersion limit for the classical solutions of the quantum Navier-Stokes equations is also established with certain convergence rates. The proof is based on a new effective velocity which converts the quantum Navier-Stokes equations into a parabolic system, and some elaborate estimates to derive the uniform-in-time positive lower and upper bounds on the specific volume.

This paper concerns the Euler-Poisson system in an annulus with finite radius. The dynamical stability of radially symmetric transonic shock solutions to the Euler-Poisson system is transformed into the global well-posedness of a free boundary problem for a second-order quasilinear hyperbolic equation. One of the crucial ingredients of the analysis is to establish an energy estimate for the associated initial boundary value problem. The steady radial transonic shock solutions are proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.

This paper studies the boundary value problem on the steady compressible Navier-Stokes-Fourier system in a channel domain ((0,1)times mathbb {T}^2) with a class of generalized slip boundary conditions that were systematically derived from the Boltzmann equation by Coron [9] and later by Aoki et al [1]. We establish the existence and uniqueness of strong solutions in ((L_{0}^{2}cap H^{2}(Omega ))times V^{3}(Omega )times H^{3}(Omega )) provided that the wall temperature is near a positive constant. The proof relies on the construction of a new variational formulation for the corresponding linearized problem and employs a fixed point argument. The main difficulty arises from the interplay of velocity and temperature derivatives together with the effect of density dependence on the boundary.