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Volume 17, Issue 2
Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm

Changxing Miao , Bo Zhang & Daoyuan Fang

J. Part. Diff. Eq., 17 (2004), pp. 97-121.

Published online: 2004-05

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  • Abstract
We study global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon equation in R^n with n ≥ 3. By means of Bourgain's method along with the endpoint Strichartz estimates of Keel and Tao, we prove the H^s-global well-posedness with s < 1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.
  • Keywords

Klein-Gordon equations Strichartz estimates Besov spaces wellposedness

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COPYRIGHT: © Global Science Press

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@Article{JPDE-17-97, author = {Changxing Miao , Bo Zhang and Daoyuan Fang }, title = {Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {2}, pages = {97--121}, abstract = { We study global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon equation in R^n with n ≥ 3. By means of Bourgain's method along with the endpoint Strichartz estimates of Keel and Tao, we prove the H^s-global well-posedness with s < 1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5380.html} }
TY - JOUR T1 - Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm AU - Changxing Miao , Bo Zhang & Daoyuan Fang JO - Journal of Partial Differential Equations VL - 2 SP - 97 EP - 121 PY - 2004 DA - 2004/05 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5380.html KW - Klein-Gordon equations KW - Strichartz estimates KW - Besov spaces KW - wellposedness AB - We study global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon equation in R^n with n ≥ 3. By means of Bourgain's method along with the endpoint Strichartz estimates of Keel and Tao, we prove the H^s-global well-posedness with s < 1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.
Changxing Miao , Bo Zhang and Daoyuan Fang . (2004). Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm. Journal of Partial Differential Equations. 17 (2). 97-121. doi:
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