相关论文: A nonlinear elliptic PDE from atmospheric science:…
The motion of point vortices constitutes an especially simple class of solutions to Euler's equation for two dimensional, inviscid, incompressible, and irrotational fluids. In addition to their intrinsic mathematical importance, these…
We address semigroup well-posedness of the fluid-structure interaction of a linearized compressible, viscous fluid and an elastic plate (in the absence of rotational inertia). Unlike existing work in the literature, we linearize the…
Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the…
In this paper, we present a novel center manifold reduction theorem for quasilinear elliptic equations posed on infinite cylinders. This is done without a phase space in the sense that we avoid explicitly reformulating the PDE as an…
Surface quasi geostrophy (SQG) describes the two-dimensional active transport of a temperature field in a strongly stratified and rotating environment. Besides its relevance to geophysics, SQG bears formal resemblance with various flows of…
We consider the forced surface quasi-geostrophic equation with supercritical dissipation. We show that linear instability for steady state solutions leads to their nonlinear instability. When the dissipation is given by a fractional…
In this paper we consider a degenerate pseudoparabolic equation for the wetting saturation of an unsaturated two-phase flow in porous media with dynamic capillary pressure-saturation relationship where the relaxation parameter depends on…
We study the dynamics of quantized superfluid vortices on axisymmetric compact surfaces with no holes, where the total vortex charge must vanish and the condition of irrotational flow forbids distributed vorticity. A conformal…
We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to…
The equations governing atmospheric flows are nonlinear. Consequently, the hierarchy of cumulant equations is not closed. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing from fluid content…
We study phase behaviour of a model fluid confined between two unlike parallel walls in the presence of long range (dispersion) forces. Predictions obtained from macroscopic (geometric) and mesoscopic arguments are compared with numerical…
We consider the problem of solving partial differential equations (PDEs) in domains with complex microparticle geometry that is impractical, or intractable, to model explicitly. Drawing inspiration from volume rendering, we propose tackling…
Recent advances in cold-atom platforms have made real-time dynamics accessible, renewing interest in the motion of superfluid vortices in two-dimensional domains. Here we show that the energy and the trajectories of arbitrary vortex…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We construct steady non-spherical bubbles and drops, which are traveling wave solutions to the axisymmetric two-phase Euler equations with surface tension, whose inner phase is a bounded connected domain. The solutions have a uniform…
We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in $\mathbb R^{3}$. The regularization is geometric, and has a natural variational interpretation.
We present a formal derivation of the inviscid 3D quasi-geostrophic system (QG) from primitive equations on a bounded, cylindrical domain. A key point in the derivation is the treatment of the lateral boundary and the resulting boundary…