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* Scaling is <math>s_c = d/2 - 2/3</math>. * For <math>d>2</math> LWP is known for <math>s \geq d/2 - 2/3</math> by Strichartz estimates. This is sharp by scaling argumentsin both the focusing and defocusing cases [[CtCoTa-p2]] * For <math>d=2</math> LWP is known for <math>s \geq 5/12</math> by Strichartz estimates. This is sharp by concentration arguments in the focusing case; the defocusing case is open. ** In the defocusing case one has GWP for <math>s > 2/3</math> [[Fo-p]] * For <math>d=1</math> one has LWP for <math>s\geq 1/4</math> by energy estimates and Sobolev (solution is in <math>L^4_x</math>). Below this regularity one cannot even make sense of the solution as a distribution. [[Category:Wave]] [[Category:Equations]]

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