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• W2063013454 abstract "We verify the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=3> <mml:semantics> <mml:mn>3</mml:mn> <mml:annotation encoding=application/x-tex>3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional Glassey conjecture on asymptotically flat manifolds <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis double-struck upper R Superscript 1 plus 3 Baseline comma German g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(mathbb {R}^{1+3},mathfrak {g})</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where the metric <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a certain small space-time perturbation of the flat metric, as well as the nontrapping asymptotically Euclidean manifolds. Moreover, for radial asymptotically flat manifolds <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis double-struck upper R Superscript 1 plus n Baseline comma German g right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mo>,</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(mathbb {R}^{1+n},mathfrak {g})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than-or-equal-to 3> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:mn>3</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>nge 3</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we verify the Glassey conjecture in the radial case. High dimensional wave equations with higher regularity are also discussed. The main idea is to exploit local energy and KSS estimates with variable coefficients, together with the weighted Sobolev estimates including trace estimates." @default.
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• W2063013454 date "2014-09-23" @default.
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• W2063013454 title "The Glassey conjecture on asymptotically flat manifolds" @default.
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