Fractal analysis of Hopf bifurcation for a class of completely integrable nonlinear Schrödinger Cauchy problems.
Fractal Weyl laws for quantum resonances
Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations
MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf GorenfloThere is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving process, corresponding...
Fredholm determinants
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
Free boundary problem for the equations of magnetohydrodynamic incompressible viscous fluid
The existence of a global motion of magnetohydrodynamic fluid in a domain bounded by a free surface and under the external electrodynamic field is proved. The motion is such that the velocity and magnetic field are small in the H³-space.
Free Boundary Problems Associated with Multiscale Tumor Models
The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...
Free boundary problems for nonstationary Navier-Stokes equations [Book]
Free boundary problems for Stoke's flows and finite element methods
Free surface flow over an obstacle. Theoretical study of the fluvial case.
From discrete Boltzmann equation to compressible linearized Euler equations.
From the BGK model to the Navier–Stokes equations
Front d’onde à l’infini pour l’équation de Schrödinger
Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem
We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic.
Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation.
Further extended sinh-cosh and sin-cos methods and new nontraveling wave solutions of the -dimensional dispersive long wave equations.
Gain of regularity for a Korteweg-de Vries--Kawahara type equation.
Gain of regularity for equations of KdV type
Gasdynamic regularity: some classifying geometrical remarks.
Gaussian Decay of the Magnetic Eigenfunctions.
Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.