Related papers: A fractional Yamabe flow and some applications

We study the Yamabe problem on open manifolds of bounded geometry and show that under suitable assumptions there exist Yamabe metrics, i.e. conformal metrics of constant scalar curvature. For that, we use weighted Sobolev embeddings.

In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case.…

We study the asymptotic convergence of solutions as $t\rightarrow\infty$ of $\partial_t u=-f(u)+\int f(u)$, a nonlocal differential equation that is formally a gradient flow in a constant-mass subspace of $L^2$ arising from simplified…

We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable…

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions.…

In this paper, we study the geometric aspects of ball packings on $(M,\mathcal{T})$, where $\mathcal{T}$ is a triangulation on a 3-manifold $M$. We introduce a combinatorial Yamabe invariant $Y_{\mathcal{T}}$, depending on the topology of…

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows and inhomogeneous turbulence fit…

For an embedded conformal hypersurface with boundary, we construct critical order local invariants and their canonically associated differential operators. These are obtained holographically in a construction that uses a singular Yamabe…

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…

We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing…

This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…

This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…

We study a conformal flow for compact Riemannian manifolds of dimension greater than two with boundary. Convergence to a scalar-flat metric with constant mean curvature on the boundary is established in dimensions up to seven, and in any…

For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…

In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the…

In this paper, we introduce the notion of dynamical coherence for a partially hyperbolic flow $(\varphi^t)$ on a smooth compact manifold $M$, and prove it under the assumption that there exists a compact foliation with trivial holonomy…

This work is concerned with the gradient flow of absolutely $p$-homogeneous convex functionals on a Hilbert space, which we show to exhibit finite ($p<2$) or infinite extinction time ($p \geq 2$). We give upper bounds for the finite…

The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…

Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…

We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize…