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Cauchy problem of nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2
Applied mathematics Cauchy problem nonlinear Schrodinger equation local well-posedness scaling limit
2011/10/15
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
On the Cauchy Problem for nonlinear Schrödinger equations with rotation
Nonlinear Schr¨odinger equation Bose-Einstein condensation rotation
2010/12/9
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr¨odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a wel...
Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$
Nonlinear Schr¨odinger equation Continuous dependence
2010/12/3
We consider the Cauchy problem for the nonlinear Schr¨odinger equation i@tu + u = 1u + 2|u| u in RN, in Hs subcritical case 0 < 4 N−2s , when 0 < s < N 2 and 0 < +1, when s > N 2 . We...
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
class of two-dimensional nonlocal nonlinear wave equatio elastic materials
2010/12/1
This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing antiplane shear motions in nonlocal elasticity.