Pseudoconformal Transformation: Difference between revisions
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The pseudoconformal transformation | The pseudoconformal transformation | ||
<math> u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{i |y|^2}{4t} u ( - \frac{1}{\tau} , \frac{y}{\tau}) </math> | <math> u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{\frac{i |y|^2}{4t}} u ( - \frac{1}{\tau} , \frac{y}{\tau}) </math> | ||
maps solutions of the [[Mass critical NLS|mass critical NLS]] to solutions. The pseudoconformal image of a [[Soliton|soliton]] is an explicit [[Blowup solution|blowup solution]]. The pseudoconformal transformation is an isometry on <math>L^2_x</math> and on <math>L^2</math>-admissible [[Strichartz estimates|Strichartz spaces]] <math>L^q_\tau L^r_y</math>. | maps solutions of the [[Mass critical NLS|mass critical NLS]] to solutions. The pseudoconformal image of a [[Soliton|soliton]] is an explicit [[Blowup solution|blowup solution]]. The pseudoconformal transformation is an isometry on <math>L^2_x</math> and on <math>L^2</math>-admissible [[Strichartz estimates|Strichartz spaces]] <math>L^q_\tau L^r_y</math>. | ||
Revision as of 02:03, 31 July 2006
The pseudoconformal transformation
Failed to parse (syntax error): {\displaystyle u(t,x) \to v(\tau, y) = \frac{|\tau|^{-\frac{d}{2}} e^{\frac{i |y|^2}{4t}} u ( - \frac{1}{\tau} , \frac{y}{\tau}) }
maps solutions of the mass critical NLS to solutions. The pseudoconformal image of a soliton is an explicit blowup solution. The pseudoconformal transformation is an isometry on and on -admissible Strichartz spaces .
