In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two dimensional ...

We derive a detailed, pointwise description of the asymptotic behavior of solutions of the Cauchy problem for the Navier-Stokes equations of compressible flow in several space dimensions, with initial ...

BUFFALO, N.Y. — Last year, onlookers observed a startling site on China’s Qiantang River: waves forming a grid-like pattern. Dubbed the “matrix tide,” this complex wave pattern was caused by the river ...