Related papers: An improved Liouville type theorem for Beltrami fl…
Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…
This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…
Recently, two of these authors construct dissipative continuous (weak) solutions to the incompressible Euler equations on the three-dimensional torus $\mathbb T^3$. The building blocks in their proof are Beltrami flows, which are inherently…
Sinusoidal flows are an important class of explicit stationary solutions of the two-dimensional incompressible Euler equations on a flat torus. For such flows, the steam functions are eigenfunctions of the negative Laplacian. In this paper,…
We consider a phase field model for the flow of two partly miscible incompressible, viscous fluids of Non-Newtonian (power law) type. In the model it is assumed that the densities of the fluids are equal. We prove existence of weak…
The LBM is combined with the Volume Penalization (VP LBM) approach to simulate flows in the presence of obstacles. The single relaxation time LBM and the multiple relaxation time LBM are used. For cases where the fluid motion is enhanced by…
In this paper, we are concerned with Liouville-type theorems for the nonlinear elliptic equation {equation*} \Delta^2 u=|x|^a |u|^{p-1}u\;\ {in}\;\ \Omega, {equation*}where $a \ge 0$, $p>1$ and $\Omega \subset \mathbb{R}^n$ is an unbounded…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flux for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary…
In this paper, we establish three Arnold-type stability theorems for steady or rotating solutions of the incompressible Euler equation on a sphere. Specifically, we prove that if the stream function of a flow solves a semilinear elliptic…
In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(\rho, \mathbf{u})$ satisfies suitable conditions.
In this paper, we study the dual Anomaly flow, which is a dual version of the Anomaly flow under T-duality. A family of monotone functionals is introduced and used to estimate the dilaton function along the flow. Many examples and…
Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.
We establish a Sturm{Liouville theorem for quadratic operator pencils counting their unstable real roots, with applications to stability of waves. Such pencils arise, for example, in reduction of eigenvalue systems to higher-order scalar…
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…
We propose a new stability analysis of the Vectorial Lattice-Boltzmann Method (VLBM). The VLBM is a variant of the LBM with extended stability features: it allows to handle compressible flows with shock waves, while the LBM is limited to…
In this note we will adapt Topping's $\mathcal{L}$-optimal transportation theory for Ricci flow to a more general situation, i.e. to a closed manifold $(M,g_{ij}(t))$ evolving by $\partial_tg_{ij}=-2S_{ij}$, where $S_{ij}$ is a symmetric…
We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a…
Motivated by the Hamilton's Ricci flow, we define the homogeneous flow of a parallelizable manifold and show the long time existence and uniqueness of its solutions on $[0,\infty).$ Using this flow, we outline a simple proof of the Poincare…
In this paper we prove a Liouville type theorem for generalized stationary Navier-Stokes systems in $\Bbb R^3$, which model non-Newtonian fluids, where the Laplacian term $\Delta u$ is replaced by the corresponding non linear operator…