16,349 research outputs found
Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions
The global classical solution to the incompressible Navier-Stokes-Fourier
equation with small initial data in the whole space is constructed through a
zero Knudsen number limit from the solutions to the Boltzmann equation with
general collision kernels. The key point is the uniform estimate of the Sobolev
norm on the global solutions to the Boltzmann equation.Comment: 21 page
Existence and convexity of local solutions to degenerate hessian equations
In this work, we prove the existence of local convex solution to the
degenerate Hessian equationComment: corrections some typos in this versio
Ultra-analytic effect of Cauchy problem for a class of kinetic equations
The smoothing effect of the Cauchy problem for a class of kinetic equations
is studied. We firstly consider the spatially homogeneous non linear Landau
equation with Maxwellian molecules and inhomogeneous linear Fokker-Planck
equation to show the ultra-analytic effects of the Cauchy problem. Those
smoothing effect results are optimal and similar to heat equation. In the
second part, we study a model of spatially inhomogeneous linear Landau equation
with Maxwellian molecules, and show the analytic effect of the Cauchy problem.Comment: 22 pages, to appear in JD
Gevrey regularizing effect of the Cauchy problem for non-cutoff homogeneous Kac's equation
In this work, we consider a spatially homogeneous Kac's equation with a non
cutoff cross section. We prove that the weak solution of the Cauchy problem is
in the Gevrey class for positive time. This is a Gevrey regularizing effect for
non smooth initial datum. The proof relies on the Fourier analysis of Kac's
operators and on an exponential type mollifier
Long time well-posdness of the Prandtl equations in Sobolev space
In this paper, we study the long time well-posedness for the nonlinear
Prandtl boundary layer equation on the half plane. While the initial data are
small perturbations of some monotonic shear profile, we prove the existence,
uniqueness and stability of solutions in weighted Sobolev space by energy
methods. The key point is that the life span of the solution could be any large
as long as its initial date is a perturbation around the monotonic shear
profile of small size like . The nonlinear cancellation properties of
Prandtl equations under the monotonic assumption are the main ingredients to
establish a new energy estimate.Comment: In this version, reviser some typos, 43 page
Solution of the Dirichlet Problem for Degenerate -Hessian Equations
In this paper, we prove the existence of -solution to the Dirichlet
problem for degenerate elliptic -Hessian equations under a
condition which is weaker than the condition .Comment: 18page
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