We first prove that the Cauchy problem of the Kawahara equation, δtu ＋ uδxu ＋βδx^3u＋γδx^5u = 0, is locally solvable if the initial data belong to H^r（R） and r〉 r≥-7/5, thus improving the known local well-...We first prove that the Cauchy problem of the Kawahara equation, δtu ＋ uδxu ＋βδx^3u＋γδx^5u = 0, is locally solvable if the initial data belong to H^r（R） and r〉 r≥-7/5, thus improving the known local well-posedness result of this equation. Next we use this local result and the method of ＂almost conservation law＂ to prove that global solutions exist if the initial data belong to H^r（R） and r〉-1/2.展开更多
基金This work is partially supported by the China National Natural Science Foundation(No.10471157)the second author is also supported in part by the Advanced Research Center of the Sun Yat-Sen University
文摘We first prove that the Cauchy problem of the Kawahara equation, δtu ＋ uδxu ＋βδx^3u＋γδx^5u = 0, is locally solvable if the initial data belong to H^r（R） and r〉 r≥-7/5, thus improving the known local well-posedness result of this equation. Next we use this local result and the method of ＂almost conservation law＂ to prove that global solutions exist if the initial data belong to H^r（R） and r〉-1/2.
