A quasilinear parabolic system with nonlocal boundary condition.
A Radó type theorem for -harmonic functions in the plane.
A rapid convergence method for a singular perturbation problem
A reaction-diffusion equation on a net-shaped thin domain
A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types
We study the Landau-Lifshitz model for the energy of multi-scale transition layers – called “domain walls” – in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors that differ by an angle . Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The...
A Reduced Model for Flame-Flow Interaction
The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order...
A refinement of the Poincaré inequality for Kolmogorov operators on .
A regularity criterion for 3D micropolar fluid flows in terms of one partial derivative of the velocity
We prove a regularity criterion for micropolar fluid flows in terms of one partial derivative of the velocity in a Morrey-Campanato space.
A regularity criterion for the 2D MHD and viscoelastic fluid equations
This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field B, respectively the local deformation gradient F, satisfies for 1/p + 1/q = 1 and 2 < p ≤ ∞, then the corresponding local solution can be extended beyond time T.
A regularity criterion for the 3D density-dependent incompressible flow of liquid crystals with vacuum
We consider the Cauchy problem for the 3D density-dependent incompressible flow of liquid crystals with vacuum, and provide a regularity criterion in terms of u and ∇d in the Besov spaces of negative order. This improves a recent result of Fan-Li [Comm. Math. Sci. 12 (2014), 1185-1197].
A regularity criterion for the dissipative quasi-geostrophic equations
A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient
The incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.
A regularity property of -harmonic functions.
A regularity result for a convex functional and bounds for the singular set
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1. We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give a bound on the Hausdorff dimension of the singular set of minimizers.
A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations
A regularity result for p-harmonic equations with measure data.
We examine the p-harmonic equation div |grad u|(p-2). grad u = mu, where mu is a bounded Radon measure. We determine a range of p's for which solutions to the equation verify an a priori estimate. For such p's we also prove a higher integrability result.
A regularity theorem for curvature flows.
A remark concerning the dependence on the initial data of the solution of the Cauchy problem for a linear equation with analytic coefficients
A Remark on a boundary contact problem in linear elasticity.
A remark on a Harnack inequality for degenerate parabolic equations