We study the global in time existence of small solutions and a sharp time decay estimate to the Cauchy problem for the modified Korteweg–de Vries equation. We consider the real-valued… Click to show full abstract
We study the global in time existence of small solutions and a sharp time decay estimate to the Cauchy problem for the modified Korteweg–de Vries equation. We consider the real-valued initial data. Also we assume that the mean value of the initial data vanishes. We present a simple proof comparing with the previous works which is based on the development of the Factorization Techniques and a new function space of solutions. Our function space yields a sharp time decay of solutions in the uniform norm.
Keywords:
korteweg vries;
approach obtaining;
time;
modified korteweg;
simplified approach;
vries equation
Journal Title: Journal of Mathematical Physics
Year Published: 2025
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Journal Title: Journal of Mathematical Physics
Year Published: 2025
Link to full text (if available)
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recommendations!