Global solvabilty for nonlinear wave equations with singular potential

In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case p > 1 + √ 2 we establish the small data global existence result. The approach is based on appropriate conformal energy estimate in combination with Hardy inequality for conformal energy on space like surfaces.

[1]  Qi S. Zhang,et al.  Finite time blow up for critical wave equations in high dimensions , 2004, math/0404055.

[2]  Yi Zhou.  Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions* , 2007 .

[3]  Wei Dai,et al.  Long-time existence for semilinear wave equations with the inverse-square potential , 2021, Journal of Differential Equations.

[4]  Mengyun Liu,et al.  Lifespan estimates for semilinear wave equations with space dependent damping and potential , 2021, Calculus of Variations and Partial Differential Equations.

[5]  A. Tahvildar-Zadeh,et al.  $L^p$ Estimates for the wave equation with the inverse-square potential , 2002 .

[6]  H. Kubo.  On the critical decay and power for semilinear wave equations in odd space dimensions , 1994 .

[7]  H. Kubo,et al.  Asymptotic behaviors of radially symmetric solutions of $B""(Bu = |u|P for super critical values p in even space dimensions , 1994 .

[8]  H. Takamura,et al.  The blow-up and lifespan of solutions to systems of semilinear wave equation with critical exponents in high dimensions , 2011, Differential and Integral Equations.

[9]  D. Tataru.  Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation , 2000 .

[10]  Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential , 2005, math/0503171.

[11]  Thomas C. Sideris,et al.  Nonexistence of global solutions to semilinear wave equations in high dimensions , 1984 .

[12]  Borislav Yordanov,et al.  Finite-Time Blowup for Wave Equations with a Potential , 2005, SIAM J. Math. Anal..

[13]  V. Georgiev.  Semilinear hyperbolic equations , 2005 .

[14]  V. Georgiev,et al.  SUPERCRITICAL SEMILINEAR WAVE EQUATION WITH NON-NEGATIVE POTENTIAL , 2001 .

[15]  Weighted Strichartz estimates and global existence for semilinear wave equations , 1997, math/9912206.

[16]  Yi Zhou,et al.  An elementary proof of Strauss conjecture , 2014 .

[17]  C. Miao,et al.  STRICHARTZ ESTIMATES FOR WAVE EQUATION WITH INVERSE SQUARE POTENTIAL , 2013, 1312.1745.

[18]  F. John.  Blow-up of solutions of nonlinear wave equations in three space dimensions , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[19]  B. Simon.  Essential self-adjointness of Schrödinger operators with positive potentials , 1973 .

[20]  W. Strauss,et al.  Existence and blow up of small amplitude nonlinear waves with a negative potential , 1997 .

[21]  Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential , 2002, math/0207152.