On questions of decay and existence for the viscous Camassa–Holm equations
On radial limit functions for entire solutions of second order elliptic equations in R2.
Given a homogeneous elliptic partial differential operator L of order two with constant complex coefficients in R2, we consider entire solutions of the equation Lu = 0 for whichlimr→∞ u(reiφ) =: U(eiφ)exists for all φ ∈ [0; 2π) as a finite limit in C. We characterize the possible "radial limit functions" U. This is an analog of the work of A. Roth for entire holomorphic functions. The results seems new even for harmonic functions.
On radially symmetric solutions of some chemotaxis system
This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.
On rates of propagation for Burgers’ equation
We give asymptotic formulae for the propagation of an initial disturbance of the Burgers’ equation.
On ratio improvement of Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system
This paper concerns improving Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes system, in the sense of multiplying certain negative powers of scaling invariant norms.
On rational and periodic solutions of stationary KdV equations.
On reaction-diffusion systems.
On real interpolation, finite differences, and estimates depending on a parameter for discretizations of elliptic boundary value problems.
On realizations related to Weyl operators.
On recent progress for the stochastic Navier Stokes equations
We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity, exponential...
On reducing bandwidth of matrices in the Go-Away algorithm for regular grids.
On reduction of some classes of partial differential equations to equations with fewer variables and exact solutions.
On reflection of shock front in multidimensional space
On regular points in Burgers turbulence with stable noise initial data
On regularity of solutions of nonlinear parabolic systems
On regularity of solutions to some problems of mathematical physics
On regularity of solutions to systems of partial differential equations which are locally close to elliptic systems of linear equations with constant coefficients. II.
On regularity of stationary solutions to the Navier-Stokes equation in 3D torus.
On representation of a solution to a modified Cauchy problem.
On representations of Lie algebras of a generalized Tavis-Cummings model.