Geodesic
On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg--de Vries Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 51-60

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We establish conditions on the initial data under which the Cauchy problem for the Korteweg–de Vries equation does not admit a solution global in $t>0$. The proof of the results is based on the nonlinear capacity method (Dokl. RAN, 357:5 (1997), 592–594). In closing, we provide an example.
Keywords: blow-up, KdV equation, initial-boundary value problem, Cauchy problem, nonlinear capacity. 
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     author = {S. I. Pokhozhaev},
     title = {On the {Nonexistence} of {Global} {Solutions} of the {Cauchy} {Problem} for the {Korteweg--de} {Vries} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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S. I. Pokhozhaev. On the Nonexistence of Global Solutions of the Cauchy Problem for the Korteweg--de Vries Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 4, pp. 51-60. http://geodesic.mathdoc.fr/item/FAA_2012_46_4_a3/