Journal of Mathematical Fluid Mechanics最新文献

The present paper studies a two-component mathematical model representing shallow-water wave propagation primarily in equatorial ocean regions, incorporating the effects of weak Coriolis force and equatorial undercurrent. We start with the Green–Naghdi type equations under the weak Coriolis and equatorial undercurrent effects from the Euler equations, then the two-component Camassa–Holm system with the two effects is derived by truncating asymptotic expansions of the quantities to the appropriate order. Analytically, we study the mathematical properties of the solutions to the two-component Camassa–Holm system including the ill-posedness of the solutions in Besov spaces (B^{s}_{p,infty }times B^{s-1}_{p,infty }) with (1le ple infty ) and (s>max left{ 2+frac{1}{p},frac{5}{2}right} ), the Hölder continuity of the data-to-solution map in Besov spaces (B^{s}_{p,r}times B^{s-1}_{p,r}) with (1le p,rle infty ) and (s>max left{ 2+frac{1}{p},frac{5}{2}right} ). We then investigate the Gevrey regularity and analyticity of the system in ({G_{delta ,s}^{gamma }}times {G_{delta ,s-1}^{gamma }}) with (delta ge 1, nu>gamma >0) and (s>frac{5}{2}). Finally, we provide the persistence properties and the spatial asymptotic profiles of the solutions in weighted spaces (L ^ p_{phi }=L^p(mathbb {R},phi ^pdx)).

We prove two Liouville-type theorems for the stationary Navier–Stokes equations in (mathbb {R}^3) under some assumptions on 1) the growth of the (L^s) mean oscillation of a potential function of the velocity field, or 2) the relative decay of the head pressure and the square of the velocity field at infinity. The main idea is to use Saint-Venant type estimates to characterize the growth of Dirichlet energy of nontrivial solutions. These assumptions are weaker than those previously known of a similar nature.

We consider the construction of linear instability of parallel shear flows, which was developed by Lin (SIAM J Math Anal 35(2):318–356, 2003). We give an alternative simple proof in Sobolev setting of the problem, which exposes the mathematical role of the Plemelj–Sochocki formula in the emergence of the instability, as well as does not require the cone condition. Moreover, we localize this approach to obtain an approximation of the Kelvin–Helmholtz instability of a flat vortex sheet.

We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. By using the Lagrangian structure of the system to homogenize the free boundary conditions coupled with the semigroup method of the linear operator, we establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no compatibility conditions of the accelerated velocity on the initial data are required.

The article deals with the 3D stationary Stokes system under traction boundary conditions, in interior and exterior domains. In the interior domain case, we obtain solutions with (W^{2,p})-regular velocity and (W^{1,p})-regular pressure globally in the domain, under suitable assumptions on the data. In the exterior domain case we construct two solutions classes, both of them consisting of functions which are (W^{2,p})–(W^{1,p})-regular in any vicinity of the boundary, with (p in (1, infty )) determined by the assumptions on the data. In addition the velocity part of these solutions is (L^s)-integrable near infinity, for some (s>3), provided that the right-hand side of the Stokes system is (L^p)-integrable near infinity for some (p<3/2). Moreover, the velocity part of the solutions in one of the two classes satisfies a zero flux condition on the boundary, whereas the pressure part of the solutions in the other class is (L^s)-integrable near infinity, for some (s > 3/2). The two solution classes are also uniqueness classes, one related to a zero flux condition for the velocity, the other one to decay of the pressure at infinity. This result confirms a conjecture by T. Hishida (University of Nagoya).

We show that a convex combination of the Osgood and Nagumo conditions ensures the uniqueness of the solution to the boundary value problem for a second-order nonlinear differential equation on a semi-infinite interval. A typical example of such problem is a recently derived nonlinear model for the motion of arctic gyres.

We study by a combination of analytical and numerical methods multidimensional stability and transverse bifurcation of planar hydraulic shock and roll wave solutions of the inviscid Saint Venant equations for inclined shallow-water flow, both in the whole space and in a channel of finite width, obtaining complete stability diagrams across the full parameter range of existence. Technical advances include development of efficient multi-d Evans solvers, low- and high-frequency asymptotics, explicit/semi-explicit computation of stability boundaries, and rigorous treatment of channel flow with wall-type physical boundary. Notable behavioral phenomena are a novel essential transverse bifurcation of hydraulic shocks to invading planar periodic roll-wave or doubly-transverse periodic herringbone patterns, with associated metastable behavior driven by mixed roll- and herringbone-type waves initiating from localized perturbation of an unstable constant state; and Floquet-type transverse “flapping” bifurcation of roll wave patterns.

This paper concerns the initial-boundary-value problem of the compressible Navier-Stokes-Poisson equations subject to large and non-flat doping profile in 3D bounded domain, where the velocity admits slip boundary condition. The global existence of strong solutions and smooth solutions near a steady state for compressible NSP are established by using the energy estimates. In particular, an important feature is that the steady state (except velocity) and the doping profile are allowed to be large.

Several recent papers have addressed the modelling of tissue growth by multi-phase models where the velocity is related to the pressure by one of the physical laws (Stokes’, Brinkman’s or Darcy’s). While each of these models has been extensively studied, not so much is known about the connection between them. In the recent paper (David et al. in SIAM J. Math. Anal. 56(2):2090–2114, 2024), assuming the linear form of the pressure, the Authors connected two multi-phase models by an inviscid limit: the viscoelastic one (of Brinkman’s type) and the inviscid one (of Darcy’s type). Here, we prove that the same is true for a nonlinear, power-law pressure. The new ingredient is that we use the relation between the pressure p and the Brinkman potential W to deduce compactness in space of p from the compactness in space of W.

We study the stationary motion of an incompressible Navier–Stokes fluid past obstacles in (mathbb {R}^{3}), subject to the provided boundary velocity (u_{b}), external force (f = textrm{div} F), and nonzero constant vector (k {e_1}) at infinity. We first prove that the existence of at least one very weak solution u in (L^{3}(Omega ) + L^{4}(Omega )) for an arbitrary large (F in L^{3/2}(Omega ) + L^{2}(Omega )) provided that the flux of (u_{b}) on the boundary of each body is sufficiently small with respect to the viscosity (nu ). Moreover, we establish weak- and strong-regularity results for very weak solutions. Consequently, our existence and regularity results enable us to prove the existence of a weak solution satisfying (nabla u in L^{r}(Omega )) for a given (F in L^{r}(Omega )) with (3/2 le r le 2), and a strong solution satisfying (nabla ^{2} u in L^{s}(Omega )) for a given (f in L^{s}(Omega )) with (1 < s le 6/5), respectively.