Related papers: Instability of strong regular reflection and count…
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law and prove a global…
The interaction of a shock wave with a localized constriction in a straight conduit is investigated by systematically varying the blockage ratio in the range 0.35-0.75, the normalized constriction length in the range 0.25-2, and the…
Explicit solutions of the non-constant semi-dynamical reflection equation are constructed, together with suitable parametrizations of their structure matrices. Considering the semi-dynamical reflection equation with rational non-constant…
When propagated action potentials in cardiac tissue interact with local heterogeneities, reflected waves can sometimes be induced. These reflected waves have been associated with the onset of cardiac arrhythmias, and while their generation…
This paper is devoted to the structural stability of a transonic shock passing through a flat nozzle for two-dimensional steady compressible flows with an external force. We first establish the existence and uniqueness of one dimensional…
Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the…
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…
In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave…
This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…
We are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and…
In this paper we study the regularity of weak solutions to systems of p-Stokes type, describing the motion of some shear thinning fluids in certain steady regimes. In particular we address the problem of regularity up to the boundary…
Global resonance is a mechanism by which a homoclinic tangency of a smooth map can have infinitely many asymptotically stable, single-round periodic solutions. To understand the bifurcation structure one would expect to see near such a…
The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was…
We develop a general theory of Bessel-Dunkl type diffusions in Weyl chambers associated with classical root systems. The class considered here allows time-dependent and configuration-dependent diffusion and drift coefficients, as well as…
Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…
We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…
We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney (BBM) and Boussinesq equations. An expansion shock exhibits…
This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized…
Scaling of the Reynolds stresses has been sought by many researchers, since it provides a template of universal dynamical patterns across a range of Reynolds numbers. Various statistical and normalization schemes have been attempted, but…
The principle of fractal stiffness self-similarity is expanded to encompass structures with several differently-scaled contributors to the total stiffness matrix. The generalized principle is applied to solve the problem of a fractal…