Global regularity estimates for the Boltzmann equation without cut-off
Cyril Imbert, Luís Silvestre
Abstract
We derive <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript normal infinity"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mi mathvariant="normal"> ∞ </mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">C^\infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a priori estimates for solutions of the inhomogeneous Boltzmann equation without cut-off, conditional to pointwise bounds on their mass, energy and entropy densities. We also establish decay estimates for large velocities, for all derivatives of the solution.
Topics & Concepts
MathematicsBoltzmann equationA priori and a posterioriBoltzmann constantBoltzmann's entropy formulaEntropy (arrow of time)Applied mathematicsBoltzmann machineMathematical analysisStatistical physicsThermodynamicsPhysicsArtificial neural networkMachine learningComputer scienceEpistemologyPhilosophyGas Dynamics and Kinetic TheoryNavier-Stokes equation solutionsNumerical methods in inverse problems