Almost Global Existence for Some Semilinear Wave Equations with Almost Critical Regularity

作者：Fang, Daoyuan; Wang, Chengbo^*

来源：Communications in Partial Differential Equations, 2013, 38(9): 1467-1491.

DOI：10.1080/03605302.2013.803482

• Angular regularity
• Generalized Strichartz estimates
• Semilinear wave equation
• Strichartz estimates

For any subcritical index of regularity s>3/2, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space H(s)xH(s-1) with certain angular regularity. The lifespan is known to be sharp in general. The main new ingredient in the proof is an endpoint version of the generalized Strichartz estimates in the space (LtL|x|L theta 2)-L-2-L-infinity(left perpendicular0, Tright perpendicular x R-2). In the last section, we also consider the general semilinear wave equations with the spatial dimension n2 and the order of nonlinearity p >= 3.

• 出版日期2013-9-2
• 单位浙江大学