On the number of single-peak solutions of the nonlinear Schrödinger equation
On the Numerical Solution of the Equation ....-(....) = f and Its Discretizations, I.
On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy...
On the one class of hyperbolic systems.
On the optimality of velocity averaging lemmas
On the Origin of Chaos in the Belousov-Zhabotinsky Reaction in Closed and Unstirred Reactors
We investigate the origin of deterministic chaos in the Belousov–Zhabotinsky (BZ) reaction carried out in closed and unstirred reactors (CURs). In detail, we develop a model on the idea that hydrodynamic instabilities play a driving role in the transition to chaotic dynamics. A set of partial differential equations were derived by coupling the two variable Oregonator–diffusion system to the Navier–Stokes equations. This approach allows us to shed light on the correlation between chemical oscillations...
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of these models have a critical mass such that the solutions exist globally in time if the mass is less than and above which there are solutions which blowup in finite time. The main tools, in particular the free energy, and the idea of the methods are set out. A number of open questions are also...
On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations
In this paper, we deal with the optimal choice of the parameter for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter for various problem parameters (Reynolds number, mesh refinement) and especially for...
On the periodic KdV equation in weighted Sobolev spaces
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...
On the Plasma-Charge problem
This short report is a review on recent results of S. Caprino, C. Marchioro, E. Miot and the author on the initial value problem associated to the evolution of a continuous distribution of charges (plasma) in presence of a finite number of point charges.
On the point limit of the Pauli-Fierz model
On the problem of the Marangoni-to-Prandtl boundary layer transition.
On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions.
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
On the rate of convergence of a collocation projection of the KdV equation
Based on estimates for the KdV equation in analytic Gevrey classes, a spectral collocation approximation of the KdV equation is proved to converge exponentially fast.
On the real analyticity of the scattering operator for the Hartree equation
We study the real analyticity of the scattering operator for the Hartree equation . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear...
On the regular solutions for some classes of Navier-Stokes equations
On the Regularity Conditions for the Navier-Stokes and Related Equations.
On the regularity for solutions of the micropolar fluid equations