Yukawa-type system: Difference between revisions
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Marco Frasca (talk | contribs) m (Activated references and corrected an error into equations) |
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<math>i \partial_t^{}u + \Delta u = -A u</math> | <math>i \partial_t^{}u + \Delta u = -A u</math> | ||
<math>\Box A = m^2_{} A + |u|2</math> | <math>\Box A = m^2_{} A + |u|^2</math> | ||
for <math>d=3</math>. A represents the meson field, while u is the nucleon field. | for <math>d=3</math>. <math>A</math> represents the meson field, while <math>u</math> is the nucleon field. | ||
Global well posedness in the energy class <math>(H^1, H^1 x L^2)</math> is in [Bch1984], [BlChd1978], [FuTs1978], [HaWl1987]. Modified wave operators were constructed for large energy data at infinity in [GiVl-p2]. | Global well posedness in the energy class <math>(H^1, H^1 x L^2)</math> is in [[Bch1984]], [[BlChd1978]], [[FuTs1978]], [[HaWl1987]]. Modified wave operators were constructed for large energy data at infinity in [[GiVl-p2]]. | ||
With positive mass m=1, global well-posedness can be pushed to <math>(H^s, H^m x H^{m-1})</math> whenever <math>1 \geq s,m > 7/10</math> and <math>s+m > 3/2 </math>[Pe-p2]. | With positive mass m=1, global well-posedness can be pushed to <math>(H^s, H^m x H^{m-1})</math> whenever <math>1 \geq s,m > 7/10</math> and <math>s+m > 3/2 </math>[[Pe-p2]]. | ||
[[Category:Equations]] | [[Category:Equations]] | ||
Latest revision as of 13:39, 24 July 2007
for . represents the meson field, while is the nucleon field.
Global well posedness in the energy class is in Bch1984, BlChd1978, FuTs1978, HaWl1987. Modified wave operators were constructed for large energy data at infinity in GiVl-p2.
With positive mass m=1, global well-posedness can be pushed to whenever and Pe-p2.
