相关论文: Global existence for the p-Sobolev flow

We derive global gradient estimates for $W^{1,p}_0(\Omega)$-weak solutions to quasilinear elliptic equations of the form $$ \mathrm{div\,}\mathbf{a}(x,u,Du)=\mathrm{div\,}(|F|^{p-2}F) $$ over $n$-dimensional Reifenberg flat domains. The…

This article is a continuation of earlier work [R.L. Huang and Y.H. Ye, On the second boundary value problem for a class of fully nonlinear flows I, to appear in International Mathematics Research Notices], where the long time existence and…

We derive moment estimates and a strong limit theorem for space inverses of stochastic flows generated by jump SDEs with adapted coefficients in weighted H\"older norms using the Sobolev embedding theorem and the change of variable formula.…

This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and…

In this paper, we focus on the two-dimensional surface quasi-geostrophic equation with fractional horizontal dissipation and vertical thermal diffusion which represents a general case of the classical surface quasi-geostrophic equation. On…

We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain $\mathbb T\times \mathbb R$. We prove a bound for general nonlinear interactions, which, for several fluid equations, reduces the…

Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show…

In this paper, we consider a non-local diffusion equation involving the fractional $p(x)$-Laplacian with nonlinearities of variable exponent type. Employing the sub-differential approach we establish the existence of local solutions. By…

This paper presents existence and uniqueness results for a class of parabolic systems with non linear diffusion and nonlocal interaction. These systems can be viewed as regular perturbations of Wasserstein gradient flows. Here we extend…

The goal of this paper is to discuss some of the results in [31] and [32] and expand upon the work there by proving a global weak existence result as well as a first bubbling analysis in finite time. In addition, an alternative local…

In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave…

We show that the pluriclosed flow preserves generalized K\"ahler structures with the extra condition $[J_+,J_-] = 0$, a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a…

We establish the unique solvability of solutions in Sobolev spaces to linear parabolic equations in a more general form than those in the literature. A distinguishing feature of our equations is the inclusion of a half-order time derivative…

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…

In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the…

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of…

In this paper we prove a characterization of $p$-hyperbolic ends on complete Riemannian manifolds which carries a Sobolev type inequality.

Our goal in this paper is to prove the global existence of a classical solution for the isentropic nozzle flow. Regarding this problem, there exist some global existence theorems of weak solutions. However, that of classical solutions does…

In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator. The approach is based on the concavity…

We consider the two-dimensional, $\beta$-plane, vorticity equations for an incompressible flow, where the zonally averaged flow varies on scales much larger than the perturbation. We prove global existence and uniqueness of the solution to…