boltzmann-equation - Page 1

The expected long time behavior of a solution of the spatially homogeneous Boltzmann equation seems to leave little room for imagination: if the initial datum has finite kinetic energy then as time t goes to the solution should converge to a Maxwellian distri bution In I thought about two related but seemingly more original problems One was the possibility to keep the energy finite but let time go to instead of then the asymptotic behavior looks a priori unclear but what is more there is good reason to suspect that there is no solution at all The other was to relax the assumption of finite energy and try to construct self similar solutions which would capture the asymptotic be havior of solutions with infinite energy and would play the role of the stable stationary laws in classical probability theory In a preliminary investigation it looked very reasonable to consider these problems in the simple setting of the spatially homogeneous Boltzmann equation with Maxwellian collision kernel

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The expected long time behavior of a solution of the spatially homogeneous Boltzmann equation seems to leave little room for imagination: if the initial datum has finite kinetic energy then as time t goes to the solution should converge to a Maxwellian distri bution In I thought about two related but seemingly more original problems One was the possibility to keep the energy finite but let time go to instead of then the asymptotic behavior looks a priori unclear but what is more there is good reason to suspect that there is no solution at all The other was to relax the assumption of finite energy and try to construct self similar solutions which would capture the asymptotic be havior of solutions with infinite energy and would play the role of the stable stationary laws in classical probability theory In a preliminary investigation it looked very reasonable to consider these problems in the simple setting of the spatially homogeneous Boltzmann equation with Maxwellian collision kernel

Cédric Villani

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The expected long time behavior of a solution of the spatially homogeneous Boltzmann equation seems to leave little room for imagination: if the initial datum has finite kinetic energy then as time t goes to the solution should converge to a Maxwellian distri bution In I thought about two related but seemingly more original problems One was the possibility to keep the energy finite but let time go to instead of then the asymptotic behavior looks a priori unclear but what is more there is good reason to suspect that there is no solution at all The other was to relax the assumption of finite energy and try to construct self similar solutions which would capture the asymptotic be havior of solutions with infinite energy and would play the role of the stable stationary laws in classical probability theory In a preliminary investigation it looked very reasonable to consider these problems in the simple setting of the spatially homogeneous Boltzmann equation with Maxwellian collision kernel

Cédric Villani

6 pages

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UPPER MAXWELLIAN BOUNDS FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION

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UPPER MAXWELLIAN BOUNDS FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION

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UPPER MAXWELLIAN BOUNDS FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION

27 pages

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FISHER INFORMATION ESTIMATES FOR BOLTZMANN S COLLISION OPERATOR

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FISHER INFORMATION ESTIMATES FOR BOLTZMANN'S COLLISION OPERATOR

Eric Carlen

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FISHER INFORMATION ESTIMATES FOR BOLTZMANN'S COLLISION OPERATOR

Eric Carlen

20 pages

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ON A NEW CLASS OF WEAK SOLUTIONS TO THE SPATIALLY HOMOGENEOUS BOLTZMANN AND

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ON A NEW CLASS OF WEAK SOLUTIONS TO THE SPATIALLY HOMOGENEOUS BOLTZMANN AND

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ON A NEW CLASS OF WEAK SOLUTIONS TO THE SPATIALLY HOMOGENEOUS BOLTZMANN AND

38 pages

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PROBABILITY METRICS AND UNIQUENESS OF THE SOLUTION TO THE BOLTZMANN EQUATION FOR A

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PROBABILITY METRICS AND UNIQUENESS OF THE SOLUTION TO THE BOLTZMANN EQUATION FOR A

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PROBABILITY METRICS AND UNIQUENESS OF THE SOLUTION TO THE BOLTZMANN EQUATION FOR A

17 pages

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SHARP ENTROPY DISSIPATION BOUNDS AND EXPLICIT RATE OF TREND TO EQUILIBRIUM FOR

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SHARP ENTROPY DISSIPATION BOUNDS AND EXPLICIT RATE OF TREND TO EQUILIBRIUM FOR

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SHARP ENTROPY DISSIPATION BOUNDS AND EXPLICIT RATE OF TREND TO EQUILIBRIUM FOR

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CONVERGENCE TO EQUILIBRIUM: ENTROPY PRODUCTION AND HYPOCOERCIVITY

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CONVERGENCE TO EQUILIBRIUM: ENTROPY PRODUCTION AND HYPOCOERCIVITY

Harold Grad

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CONVERGENCE TO EQUILIBRIUM: ENTROPY PRODUCTION AND HYPOCOERCIVITY

Harold Grad

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CERCIGNANI S CONJECTURE IS SOMETIMES TRUE AND ALWAYS ALMOST TRUE

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CERCIGNANI'S CONJECTURE IS SOMETIMES TRUE AND ALWAYS ALMOST TRUE

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CERCIGNANI'S CONJECTURE IS SOMETIMES TRUE AND ALWAYS ALMOST TRUE

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A plasma is an ensemble of particles electrons e ions i and neutrals n with di erent positions r and velocities v which move under the inﬂuence of external forces electromagnetic ﬁelds gravity and internal collision processes ionization Coulomb charge exchange etc

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A plasma is an ensemble of particles electrons e ions i and neutrals n with di erent positions r and velocities v which move under the inﬂuence of external forces electromagnetic ﬁelds gravity and internal collision processes ionization Coulomb charge exchange etc

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A plasma is an ensemble of particles electrons e ions i and neutrals n with di erent positions r and velocities v which move under the inﬂuence of external forces electromagnetic ﬁelds gravity and internal collision processes ionization Coulomb charge exchange etc

36 pages

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