Heat Conduction Dominated by Electromagnetic Radiation
Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator
We provide some new explicit expressions for the linearized non-cutoff radially symmetric Boltzmann operator with Maxwellian molecules, proving that this operator is a simple function of the standard harmonic oscillator. A detailed article is available on arXiv [15].
Hermite pseudospectral method for nonlinear partial differential equations
Hermite pseudospectral method for nonlinear partial differential equations
Hermite polynomial interpolation is investigated. Some approximation results are obtained. As an example, the Burgers equation on the whole line is considered. The stability and the convergence of proposed Hermite pseudospectral scheme are proved strictly. Numerical results are presented.
High Frequency limit of the Helmholtz Equations
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term (which does not share the...
High frequency limit of the Helmholtz equations.
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term ( which does not share the...
High-electric-field limit for the Vlasov–Maxwell–Fokker–Planck system
Higher integrability for maximal oscillatory Fourier integrals.
Higher order estimates in further dimensions for the solutions of Navier-Stokes equations
Higher-order equations of the KdV type are integrable.
Higher-order KdV-type equations and their stability.
High-order fractional partial differential equation transform for molecular surface construction
Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional...
Hodographic study of plane micropolar fluid flows.
Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
Holomorphic solution for classes of forced Korteweg-de Vries equations of fractional order
Homogénéisation et compacité par compensation
Homogénéisation variationnelle des équations d’Euler
Homogeneous and isotropic statistical solutions of the Navier-Stokes equations.
Homogeneous Cooling with Repulsive and Attractive Long-Range Potentials
The interplay between dissipation and long-range repulsive/attractive forces in homogeneous, dilute, mono-disperse particle systems is studied. The pseudo-Liouville operator formalism, originally introduced for hard-sphere interactions, is modified such that it provides very good predictions for systems with weak long-range forces at low densities, with the ratio of potential to fluctuation kinetic energy as control parameter. By numerical simulations, ...
Homogenization and diffusion asymptotics of the linear Boltzmann equation
We investigate the diffusion limit for general conservative Boltzmann equations with oscillating coefficients. Oscillations have a frequency of the same order as the inverse of the mean free path, and the coefficients may depend on both slow and fast variables. Passing to the limit, we are led to an effective drift-diffusion equation. We also describe the diffusive behaviour when the equilibrium function has a non-vanishing flux.