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The paper considers a manifold M evolving under the Ricci
ow and establishes a series of gradient
estimates for positive solutions of the heat equation on M. Among other results, we prove Li-Yau-ty...
New Bilinear Estimates for Quadratic-Derivative Nonlinear Wave Equations in 2+1 Dimensions
Bilinear Estimates Quadratic-Derivative Nonlinear
2014/12/8
This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Le...
Strichartz estimates for Dirichlet-wave equations in two dimensions with applications
Strichartz estimtes Strauss conjecture obstacles
2011/2/21
We establish the Strauss conjecture for nontrapping obstacles when the spatial dimension n is two. As pointed out in [7] this case is more subtle than n = 3 or 4 due to the fact that the arguments of ...
$L^p$-estimates of the Botlzmann Equation around a traveling local Maxwellian
Boltzmann equation Lp-stability Lp-estimate travelling local Maxwellian
2010/12/13
In this paper, we are interested in the Lp-estimates of the Boltzmann equation in the case that the distribution function stays around a travelling local Maxwellian. For this, we divide both sides of ...