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Boltzmann equation without cutoff

Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off

Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off

... Kolmogorov equation in ...Landau equation in [12] by Carrapatoso et ...the Boltzmann equation without cutoff since the gain in regularity is less clear and consists in an ...

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Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off

Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off

... Kolmogorov equation in ...Landau equation in [12] by Carrapatoso et ...the Boltzmann equation without cutoff since the gain in regularity is less clear and consists in an ...

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Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

... homogeneous Boltzmann equation without angular cutoff, ...inhomogeneous Boltzmann equation, which takes the following ...

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Contribution to the study of the homogeneous Boltzmann equation

Contribution to the study of the homogeneous Boltzmann equation

... the Boltzmann equation with moderately soft potentials From both physical and numerical standpoints, we also considered propagation of chaos, which refers to the convergence of the empirical measure of a ...

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One dimensional dissipative Boltzmann equation: measure solutions, cooling rate and self-similar profile

One dimensional dissipative Boltzmann equation: measure solutions, cooling rate and self-similar profile

... tive Boltzmann equation associated to variable hard-spheres kernel: (1) we show the optimal cooling rate of the model by a careful study of the system satisfied by the solution’s moments, (2) give existence ...

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Numerical modeling of the splitting of magnetic droplets by multiphase lattice Boltzmann equation

Numerical modeling of the splitting of magnetic droplets by multiphase lattice Boltzmann equation

... / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur. For the publisher’[r] ...

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A new deviational Asymptotic Preserving Monte Carlo method for the homogeneous Boltzmann equation

A new deviational Asymptotic Preserving Monte Carlo method for the homogeneous Boltzmann equation

... Consequently, the numerical techniques are often designed in such a way that the computa- tional cost is as low as possible. In this context, Monte Carlo methods have been the dominant approach to deal with rarefied ...

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Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings

Stability of global equilibrium for the multi-species Boltzmann equation in $L^\infty$ settings

... mono-species Boltzmann equation has been extensively studied in the per- turbative context (we refer to the discussion in [7] and the exhaustive review [19]), the only result in our knowledge of a Cauchy ...

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EQUILIBRIUM SOLUTION TO THE INELASTIC BOLTZMANN EQUATION DRIVEN BY A PARTICLES THERMAL BATH

EQUILIBRIUM SOLUTION TO THE INELASTIC BOLTZMANN EQUATION DRIVEN BY A PARTICLES THERMAL BATH

... the Boltzmann equation for inelastic hard-spheres interacting through binary collisions [18, ...the Boltzmann collision operator for inelastic hard spheres does not exhibit any non trivial steady ...

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A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation

A hybrid kinetic-fluid model for solving the gas dynamics Boltzmann-BGK equation

... on B 2 ). Otherwise, there might exist local sources or sinks of mass, momentum and energy which is obviously unphysical. We shall present a numerical strategy which respects this balance perfectly. It relies first on a ...

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Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation

Moment preserving Fourier-Galerkin spectral methods and application to the Boltzmann equation

... 3. this solution in everywhere positive for time large enough; 4. this solution f N c (t, ·) converges to a solution f (t) of the truncated Boltzmann equation ( 2.7 ) with spectral accuracy, uniformly in ...

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On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation

On the stability of equilibrium preserving spectral methods for the homogeneous Boltzmann equation

... Comput. 40, 5 (2018), A2858–A2882. [3] Cercignani, C., Illner, R., and Pulvirenti, M. The Mathematical Theory of Dilute Gases, vol. 106 of Applied Mathematical Sciences. Springer-Verlag, New York, 1994. [4] Dimarco, G., ...

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HYPOCOERCIVITY IN PHI-ENTROPY FOR THE LINEAR RELAXATION BOLTZMANN EQUATION ON THE TORUS

HYPOCOERCIVITY IN PHI-ENTROPY FOR THE LINEAR RELAXATION BOLTZMANN EQUATION ON THE TORUS

... functional without using a logarithmic Sobolev inequality or similar then exactly the same calculations would work for the equation where x is in the whole space with no confining ...

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The Boltzmann Equation for a Multi-species Mixture Close to Global Equilibrium

The Boltzmann Equation for a Multi-species Mixture Close to Global Equilibrium

... multi-species Boltzmann equation in order to deal with the full ...the Boltzmann operator which prevents the direct adaptation of standard mono-species methods ...

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Determining the potential in a wave equation without a geometric condition. Extension to the heat equation

Determining the potential in a wave equation without a geometric condition. Extension to the heat equation

... To our knowledge, using observability inequalities to solve inverse problems related to the wave equation goes back to Puel and Yamamoto [8]. Later, Komornik and Yamamoto [7] applied this method to an inverse ...

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A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation

A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation

... M C ) figure 1 (bottom left) and O(N − 1 2 ) figure 1 (bottom right). Then, the curves present a kink: it corresponds to the point where the general accuracy becomes driven by the second numer- ical method. After that ...

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Global Solutions of the Boltzmann Equation over R D near Global Maxwellians with Small Mass

Global Solutions of the Boltzmann Equation over R D near Global Maxwellians with Small Mass

... equation (1.1) ∂ t F + v · ∇ x F = B(F, F ) , where B(F, F ) is a quadratic integral operator acting on the v variable only, known as the Boltzmann collision integral. The collision integral has a rather ...

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A Fokker-Planck model of the Boltzmann equation with correct Prandtl number for polyatomic gases

A Fokker-Planck model of the Boltzmann equation with correct Prandtl number for polyatomic gases

... the Boltzmann equation that can be used [20, 2, 5, 4, 14, ...the Boltzmann equation in the transition regime, they are much simpler to be discretized and give very efficient solvers [16, 5, ...

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Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation

Spectral convergence of the generalized Polynomial Chaos reduced model obtained from the uncertain linear Boltzmann equation

... ∈ [0, T ] ⊂ R + , X ∈ Θ ⊂ R Q will be called a uncertain problem. One notices that different values of X correspond to different fully decoupled deterministic equations, so in principle there is no difficulty in solving ...

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QUANTITATIVE RATES OF CONVERGENCE TO EQUILIBRIUM FOR THE DEGENERATE LINEAR BOLTZMANN EQUATION ON THE TORUS

QUANTITATIVE RATES OF CONVERGENCE TO EQUILIBRIUM FOR THE DEGENERATE LINEAR BOLTZMANN EQUATION ON THE TORUS

... σ(Φ X t (x, v)) dt ≥ κ. This definition is again inspired from the study of the controllability of the wave equation in [ 3 , 26 ] (see Section 1.2 for more details). In this context, Han-Kwan and L´eautaud give ...

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