?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Facta.bibl.u-szeged.hu%2F75810%2F&rft.title=Regularity+properties+and+blow-up+of+the+solutions+for+improved+Boussinesq+equations&rft.creator=+Shakhmurov+Veli&rft.creator=+Shahmurov+Rishad&rft.subject=01.+Term%C3%A9szettudom%C3%A1nyok&rft.subject=01.01.+Matematika&rft.description=In+this+paper%2C+we+study+the+Cauchy+problem+for+linear+and+nonlinear+Boussinesq+type+equations+that+include+the+general+differential+operators.+First%2C+by+virtue+of+the+Fourier+multipliers%2C+embedding+theorems+in+Sobolev+and+Besov+spaces%2C+the+existence%2C+uniqueness%2C+and+regularity+properties+of+the+solution+of+the+Cauchy+problem+for+the+corresponding+linear+equation+are+established.+Here%2C+L+p+-estimates+for+a+solution+with+respect+to+space+variables+are+obtained+uniformly+in+time+depending+on+the+given+data+functions.+Then%2C+the+estimates+for+the+solution+of+linearized+equation+and+perturbation+of+operators+can+be+used+to+obtain+the+existence%2C+uniqueness%2C+regularity+properties%2C+and+blow-up+of+solution+at+the+finite+time+of+the+Cauchy+for+nonlinear+for+same+classes+of+Boussinesq+equations.+Here%2C+the+existence%2C+uniqueness%2C+L+p+-regularity%2C+and+blow-up+properties+of+the+solution+of+the+Cauchy+problem+for+Boussinesq+equations+with+differential+operators+coefficients+are+handled+associated+with+the+growth+nature+of+symbols+of+these+differential+operators+and+their+interrelationships.+We+can+obtain+the+existence%2C+uniqueness%2C+and+qualitative+properties+of+different+classes+of+improved+Boussinesq+equations+by+choosing+the+given+differential+operators%2C+which+occur+in+a+wide+variety+of+physical+systems.&rft.date=2021&rft.type=Foly%C3%B3irat&rft.type=NonPeerReviewed&rft.format=full&rft.language=hu&rft.identifier=http%3A%2F%2Facta.bibl.u-szeged.hu%2F75810%2F1%2Fejqtde_2021_089.pdf&rft.identifier=+++Shakhmurov+Veli%3B++Shahmurov+Rishad%3A+++Regularity+properties+and+blow-up+of+the+solutions+for+improved+Boussinesq+equations.++(2021)+++&rft.language=eng