The Glassey Conjecture on Asymptotically Flat Manifolds

来源 :2014年非线性偏微分方程的演化国际会议 | 被引量 : 0次 | 上传用户：wangzhao0922

【摘要】

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In this talk,we will discuss our recent work on the long time existence for small solutions to certain semilinear wave equations of type utt-Δu =|ut|p,posed on

【作者】

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Chengbo Wang

【机构】

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ZhejiangUniversity,China

【出处】

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2014年非线性偏微分方程的演化国际会议

【发表日期】

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2014年6期

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In this talk,we will discuss our recent work on the long time existence for small solutions to certain semilinear wave equations of type utt-Δu =|ut|p,posed on asymptotically flat manifolds.This problem is related with the Glassey conjecture.In the flat case(Minkowski spacetime),it is conjectured that the critical index for the problem to admit small global solutions is pc= 1+2/(n-1).It has been verified for spatial dimension two and three,as well as the radial case for all dimensions.

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