期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021; 74 (6)
This paper is devoted to the study of flows associated to non-smooth vector fields. We prove the well-posedness of regular Lagrangian flows associated......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, ; ()
We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three-dimensional Prandtl system without any struc......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, ; ()
In this paper we introduce a control variate estimator for a quantity of interest that can be expressed as the expectation of a function of a random p......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021; 74 (4)
Let (M, g) be an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and positive mass. We show that each leaf of the canonica......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020; 73 (12)
We present a new proof of the sphere covering inequality in the spirit of comparison geometry, and as a by-product we find another sphere covering ine......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020; 73 (12)
Consider aC(infinity)closed connected Riemannian manifold(M,g)with negative sectional curvature. The unit tangent bundleSMis foliated by the (weak) st......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020; 73 (7)
We consider the Ising model at its critical temperature with external magnetic field ha(15/8) on the square lattice with lattice spacing a. We show th......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2019; 72 (1)
We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl-type equations that are derive......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 0; ()
We study the Gibbs measure of mixed spherical p-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models ......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2019; 72 (4)
This paper presents some progress toward an open question proposed by P.-L. Lions [26] concerning the propagation of regularities of density patches f......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2019; 72 (5)
We prove that finite Morse index solutions to the Allen-Cahn equation in Double-struck capital R-2 have finitely many ends and linear energy growth. T......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2019; 72 (10)
This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with ......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020; 73 (3)
In this paper, we study pseudospectral bounds for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. Using the pseu......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020; 73 (1)
We derive the asymptotic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) in the exterior of the domain of inf......
期刊： COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2018; 71 (2)
In this paper, we solve a long-standing open problem: nonlinear stability of the current-vortex sheet in the ideal incompressible magnetohydrodynamics......
