A reaction-diffusion equation on a net-shaped thin domain
A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
A recursive robust Bayesian estimation in partially observed financial market
I propose a nonlinear Bayesian methodology to estimate the latent states which are partially observed in financial market. The distinguishable character of my methodology is that the recursive Bayesian estimation can be represented by some deterministic partial differential equation (PDE) (or evolution equation in the general case) parameterized by the underlying observation path. Unlike the traditional stochastic filtering equation, this dynamical representation is continuously dependent on the...
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 reduced modelling approach to the pricing of mortgage backed securities.
A refinement of the Poincaré inequality for Kolmogorov operators on .
A refinement of the radial Pohozaev identity
In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.
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 positive weak solutions of -...u = u... .
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 horizontal derivatives of the two velocity components.
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 boundary value problems on Lipschitz domains
A Regularity Result for Nonlinear Elliptic Systems.