4,390 research outputs found
Pointwise wave behavior of the Navier-Stokes equations in half space
In this paper, we investigate the pointwise behavior of the solution for the
compressible Navier-Stokes equations with mixed boundary condition in half
space. Our results show that the leading order of Green's function for the
linear system in half space are heat kernels propagating with sound speed in
two opposite directions and reflected heat kernel (due to the boundary effect)
propagating with positive sound speed. With the strong wave interactions, the
nonlinear analysis exhibits the rich wave structure: the diffusion waves
interact with each other and consequently, the solution decays with algebraic
rate.Comment: Comments and references are added and some typos are corrected.
Accepted by DCDS-
Pointwise wave behavior of the Navier-Stokes equations in half space
In this paper, we investigate the pointwise behavior of the solution for the
compressible Navier-Stokes equations with mixed boundary condition in half
space. Our results show that the leading order of Green's function for the
linear system in half space are heat kernels propagating with sound speed in
two opposite directions and reflected heat kernel (due to the boundary effect)
propagating with positive sound speed. With the strong wave interactions, the
nonlinear analysis exhibits the rich wave structure: the diffusion waves
interact with each other and consequently, the solution decays with algebraic
rate.Comment: Comments and references are added and some typos are corrected.
Accepted by DCDS-
Weak Visibility Queries of Line Segments in Simple Polygons
Given a simple polygon P in the plane, we present new algorithms and data
structures for computing the weak visibility polygon from any query line
segment in P. We build a data structure in O(n) time and O(n) space that can
compute the visibility polygon for any query line segment s in O(k log n) time,
where k is the size of the visibility polygon of s and n is the number of
vertices of P. Alternatively, we build a data structure in O(n^3) time and
O(n^3) space that can compute the visibility polygon for any query line segment
in O(k + log n) time.Comment: 16 pages, 9 figures. A preliminary version of this paper appeared in
ISAAC 2012 and we have improved results in this full versio
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