Related papers: Short-time existence for some higher-order geometr…
The aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas…
In this paper, we establish the existence of periodic orbits of a twisted geodesic flow on all low energy levels and in all dimensions whenever the magnetic field form is symplectic and spherically rational. This is a consequence of a more…
In this article we show that generally almost regular flows, introduced by Bamler and Kleiner, in closed 3-manifolds will either go extinct in finite time or flow to a collection of smooth embedded minimal surfaces, possibly with…
We employ the curve shortening flow to establish three new results on the dynamics of geodesic flows of closed Riemannian surfaces. The first one is the stability, under $C^0$-small perturbations of the Riemannian metric, of certain flat…
In [8], the gradient conjecture of R. Thom was proven for gradient flows of analytic functions on Rn. This result means that the secant at a limit point converges, so that the flow cannot spiral forever. Once the trajectory becomes…
In this paper, we propse a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed…
In this paper, we prove a pseudolocality-type theorem for $\mathcal L$-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In…
We provide existence of very weak solutions and new a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. To obtain the a-priori estimates we make use of a newly…
The classical theorem of Moser, on the existence of a normal form in the neighbourhood of a hyperbolic equilibrium, is extended to a class of real-analytic Hamiltonians with aperiodically time-dependent perturbations. A stronger result is…
We show that three-dimensional homogeneous Ricci flow solutions that admit finite-volume quotients have long-time limits given by expanding solitons. We show that the same is true for a large class of four-dimensional homogeneous solutions.…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure…
Our main is to study periodic orbits of linear and invariant flows on a real, connected Lie group. Since each linear flow $\varphi_t$ has a derivation associated $\mathcal{D}$, we show that the existence of periodic orbits of $\varphi_t$ is…
In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate…
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations of the action corresponding to a Lagrangian defined on a…
This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for…
In this work, we study the short-time existence theory of Ricci-DeTurck flow starting from rough metrics which satisfy a Morrey-type integrability condition. Using the rough existence theory, we show the preservation and improvement of…
Trans-Planckian redshifts in cosmology and outside black holes may provide windows on a hypothetical short distance cutoff on the fundamental degrees of freedom. In cosmology, such a cutoff seems to require a growing Hilbert space, but for…
We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the…
In \cite{ChauMartens} the authors proved the long-time existence of Ricci flow starting from complete bounded curvature Riemannian manifolds with scale-invariant integral curvature bounded by a dimensional constant times the inverse of the…