TY - JOUR

T1 - Long Time Dynamics of Defocusing Energy Critical 3 + 1 Dimensional Wave Equation with Potential in the Radial Case

AU - Jia, Hao

AU - Liu, Baoping

AU - Xu, Guixiang

N1 - Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/10/25

Y1 - 2015/10/25

N2 - Using the channel of energy inequalities developed by T. Duyckaerts, C. Kenig and F. Merle, we prove that, modulo a free radiation, any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 + 1 dimensions converges to the set of steady states as time goes to infinity. For generic potentials, we prove there are only finitely many steady states, and in this case, modulo some free radiation, the solution converges to one steady state as time goes to infinity.

AB - Using the channel of energy inequalities developed by T. Duyckaerts, C. Kenig and F. Merle, we prove that, modulo a free radiation, any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 + 1 dimensions converges to the set of steady states as time goes to infinity. For generic potentials, we prove there are only finitely many steady states, and in this case, modulo some free radiation, the solution converges to one steady state as time goes to infinity.

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U2 - 10.1007/s00220-015-2422-9

DO - 10.1007/s00220-015-2422-9

M3 - Article

AN - SCOPUS:84937955649

SN - 0010-3616

VL - 339

SP - 353

EP - 384

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -