Related papers: Asymptotically-consistent analytical solutions for…
We describe the asymptotic behavior of Palais-Smale sequences associated to certain Yamabe-type equations on manifolds with boundary. We prove that each of those sequences converges to a solution of the limit equation plus a finite number…
The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the…
We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is…
In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the three-dimensional isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions…
The method of matched asymptotic expansions is applied to the problem of a collisionless plasma generated by UV illumination localized in a central part of the plasma in the limiting case of small Debye length ${\lambda}_D$. A…
In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated, including external magnetic field effects. The power law, the Casson fluid, the Oldroyd-B model, the Walter…
The construction of Ekman boundary layer solutions near the non-flat boundaries presents a complex challenge, with limited research on this issue. In Masmoudi's pioneering work [Comm. Pure Appl. Math. 53 (2000), 432--483], the Ekman…
Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schr\"odinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a…
There is introduced a class of barotropic equations of state (EOS) which become polytropic of index $n = 5$ at low pressure. One then studies asymptotically flat solutions of the static Einstein equations coupled to perfect fluids having…
The 3D compressible and incompressible Euler equations with a physical vacuum free boundary condition and affine initial conditions reduce to a globally solvable Hamiltonian system of ordinary differential equations for the deformation…
We study the fully-developed, time-periodic motion of a shear-dependent non-Newtonian fluid with variable exponent rheology through an infinite pipe $\Omega:= \mathbb{R}\times \Sigma\subseteq \mathbb{R}^d$, $d\in \{2,3\}$, of arbitrary…
This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the "slow curve", those solutions are crossing a turning point…
Transport equations for heavy inertial particles in turbulent boundary layers may be derived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure…
We consider the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation $iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0, \, x\in\mathbb{R},\,t>0,$ with a step-like boundary values: $q(x,t)\to 0$ as…
This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokesflow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a slightly rough boundary of the domain. Employing…
At sufficiently high Reynolds numbers, shear-flow turbulence close to a wall acquires universal properties. When length and velocity are rescaled by appropriate characteristic scales of the turbulent flow and thereby measured in \emph{inner…
This paper investigates the asymptotic behavior of solutions to the steady pressure-free Prandtl system. By employing a modified von Mises transformation, we rigorously prove the far-field convergence of Prandtl solutions to Blasius flow. A…
Hawkes point processes are first-order non-Markovian stochastic models of intermittent bursty dynamics with applications to physical, seismic, epidemic, biological, financial, and social systems. While accounting for positive feedback loops…
In the study of low-speed or low-Froude flows of a potential gravity-driven fluid past a wave-generating object, the traditional asymptotic expansion in powers of the Froude number predicts a waveless free-surface at every order. This is…
In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…